Tempered stable Lévy motion and transient super-diffusion
The space-fractional diffusion equation models anomalous super-diffusion. Its solutions are transition densities of a stable Lévy motion, representing the accumulation of power-law jumps. The tempered stable Lévy motion uses exponential tempering to cool these jumps. A tempered fractional diffusion...
Saved in:
| Published in | Journal of computational and applied mathematics Vol. 233; no. 10; pp. 2438 - 2448 |
|---|---|
| Main Authors | , |
| Format | Journal Article |
| Language | English |
| Published |
Kidlington
Elsevier B.V
15.03.2010
Elsevier |
| Subjects | |
| Online Access | Get full text |
| ISSN | 0377-0427 1879-1778 |
| DOI | 10.1016/j.cam.2009.10.027 |
Cover
| Abstract | The space-fractional diffusion equation models anomalous super-diffusion. Its solutions are transition densities of a stable Lévy motion, representing the accumulation of power-law jumps. The tempered stable Lévy motion uses exponential tempering to cool these jumps. A tempered fractional diffusion equation governs the transition densities, which progress from super-diffusive early-time to diffusive late-time behavior. This article provides finite difference and particle tracking methods for solving the tempered fractional diffusion equation with drift. A temporal and spatial second-order Crank–Nicolson method is developed, based on a finite difference formula for tempered fractional derivatives. A new exponential rejection method for simulating tempered Lévy stables is presented to facilitate particle tracking codes. |
|---|---|
| AbstractList | The space-fractional diffusion equation models anomalous super-diffusion. Its solutions are transition densities of a stable Lévy motion, representing the accumulation of power-law jumps. The tempered stable Lévy motion uses exponential tempering to cool these jumps. A tempered fractional diffusion equation governs the transition densities, which progress from super-diffusive early-time to diffusive late-time behavior. This article provides finite difference and particle tracking methods for solving the tempered fractional diffusion equation with drift. A temporal and spatial second-order Crank–Nicolson method is developed, based on a finite difference formula for tempered fractional derivatives. A new exponential rejection method for simulating tempered Lévy stables is presented to facilitate particle tracking codes. |
| Author | Baeumer, Boris Meerschaert, Mark M. |
| Author_xml | – sequence: 1 givenname: Boris surname: Baeumer fullname: Baeumer, Boris email: bbaeumer@maths.otago.ac.nz organization: Department of Mathematics & Statistics, University of Otago, Dunedin, New Zealand – sequence: 2 givenname: Mark M. surname: Meerschaert fullname: Meerschaert, Mark M. email: mcubed@stt.msu.edu organization: Department of Statistics & Probability, Michigan State University, Wells Hall, E. Lansing, MI 48824, United States |
| BackLink | http://pascal-francis.inist.fr/vibad/index.php?action=getRecordDetail&idt=22540404$$DView record in Pascal Francis |
| BookMark | eNp9kLtqwzAUhkVJoUnaB-jmpaPdo4utuJ1K6A0CXdJZHEsyKPgSJCeQR-pz9MUq49KhQ9Cg2_8J_d-CzLq-s4TcUsgo0OJ-l2lsMwZQxn0GTF6QOV3JMqVSrmZkDlzKFASTV2QRwg4AipKKOXnY2nZvvTVJGLBqbLL5_jqekrYfXN8l2Jlk8NgFZ7shCYeYTI2r60OIt9fkssYm2JvfeUk-X56367d08_H6vn7apJozOaSsQMyxYiUUFTecGshNISTPhRFCs1xToSHnRjJbYlxbVq8KZFXFuaaUlnxJ7qZ39xg0NnX8j3ZB7b1r0Z8UY7mAOGKOTjnt-xC8rf8iFNQoSe1UlKRGSeNRlBQZ-Y_RbsCxe6ztmrPk40TaWP3orFdBR0vaGuetHpTp3Rn6B7YWgyw |
| CODEN | JCAMDI |
| CitedBy_id | crossref_primary_10_1002_jgrf_20083 crossref_primary_10_1007_s11227_024_06442_w crossref_primary_10_1080_03610926_2017_1410719 crossref_primary_10_1111_gwat_12267 crossref_primary_10_1002_fut_21647 crossref_primary_10_1016_j_jeconom_2019_06_002 crossref_primary_10_1017_S096249292000001X crossref_primary_10_1214_23_BJPS565 crossref_primary_10_12677_PM_2023_1311339 crossref_primary_10_1016_j_jcp_2014_04_024 crossref_primary_10_1080_02664763_2016_1266310 crossref_primary_10_1016_j_physa_2011_07_028 crossref_primary_10_1002_2016WR020192 crossref_primary_10_1016_j_apnum_2021_03_008 crossref_primary_10_1155_2013_878097 crossref_primary_10_2478_s13540_012_0033_0 crossref_primary_10_1515_fca_2015_0023 crossref_primary_10_1016_j_rinp_2021_104360 crossref_primary_10_1007_s10614_019_09882_2 crossref_primary_10_1007_s10444_015_9434_z crossref_primary_10_1016_j_spa_2018_08_004 crossref_primary_10_1007_s42967_024_00406_w crossref_primary_10_1103_PhysRevE_91_042124 crossref_primary_10_1515_fca_2017_0065 crossref_primary_10_1007_s10915_020_01193_1 crossref_primary_10_1007_s11071_021_06628_4 crossref_primary_10_1016_j_matcom_2020_10_016 crossref_primary_10_1016_j_chaos_2022_112547 crossref_primary_10_2139_ssrn_2651135 crossref_primary_10_1515_fca_2019_0081 crossref_primary_10_1186_s13662_019_2417_5 crossref_primary_10_1515_cmam_2017_0029 crossref_primary_10_3390_fractalfract6020053 crossref_primary_10_1016_j_apnum_2022_01_015 crossref_primary_10_1088_1742_6596_798_1_012037 crossref_primary_10_1186_s13662_017_1150_1 crossref_primary_10_1080_00207160_2020_1841175 crossref_primary_10_1016_j_physa_2013_03_018 crossref_primary_10_1137_20M1335959 crossref_primary_10_1007_s11147_018_9151_0 crossref_primary_10_1080_03081087_2023_2242563 crossref_primary_10_1088_1751_8121_ac4a1c crossref_primary_10_1239_jap_1331216840 crossref_primary_10_1051_m2an_2019052 crossref_primary_10_1140_epjst_e2014_02331_7 crossref_primary_10_1016_j_camwa_2024_11_004 crossref_primary_10_1088_1742_5468_2013_05_P05016 crossref_primary_10_1016_j_jconhyd_2013_11_002 crossref_primary_10_1002_mma_7813 crossref_primary_10_1007_s10915_017_0506_8 crossref_primary_10_1016_j_apnum_2019_05_008 crossref_primary_10_1515_fca_2017_0007 crossref_primary_10_1016_j_isatra_2017_04_005 crossref_primary_10_3390_fractalfract5040145 crossref_primary_10_1016_j_cnsns_2013_12_003 crossref_primary_10_1029_2012GL053476 crossref_primary_10_1088_1361_6560_acbf9c crossref_primary_10_1088_1748_9326_6_3_034008 crossref_primary_10_1103_PhysRevE_87_042136 crossref_primary_10_1080_01621459_2018_1447485 crossref_primary_10_1007_s10959_024_01361_1 crossref_primary_10_1016_j_physa_2014_11_049 crossref_primary_10_1080_03610918_2011_582561 crossref_primary_10_1016_j_physd_2017_12_005 crossref_primary_10_1088_1402_4896_ad837e crossref_primary_10_1002_hyp_10837 crossref_primary_10_1016_j_physa_2011_04_025 crossref_primary_10_1016_j_acha_2019_11_004 crossref_primary_10_1016_j_jhydrol_2014_02_064 crossref_primary_10_1029_2011WR011657 crossref_primary_10_1088_1742_5468_2014_09_P09023 crossref_primary_10_1016_j_jeconom_2020_11_004 crossref_primary_10_1214_EJP_v16_920 crossref_primary_10_1214_EJP_v16_909 crossref_primary_10_1007_s10955_010_9965_0 crossref_primary_10_1137_140985536 crossref_primary_10_3934_dcdss_2021149 crossref_primary_10_1002_mma_8441 crossref_primary_10_1002_mma_7343 crossref_primary_10_1007_s10915_024_02472_x crossref_primary_10_1016_j_cam_2016_09_006 crossref_primary_10_1145_3184453 crossref_primary_10_1016_j_amc_2018_02_023 crossref_primary_10_1137_130927292 crossref_primary_10_1137_17M1151791 crossref_primary_10_1080_14697688_2015_1111522 crossref_primary_10_1080_03610926_2011_552828 crossref_primary_10_1103_PhysRevE_96_052116 crossref_primary_10_1140_epjb_e2017_80400_5 crossref_primary_10_1016_j_jeconom_2018_03_016 crossref_primary_10_1103_PhysRevLett_115_110601 crossref_primary_10_3390_sym13050823 crossref_primary_10_1051_0004_6361_202451765 crossref_primary_10_1016_j_chaos_2017_03_059 crossref_primary_10_1103_PhysRevE_101_052119 crossref_primary_10_3390_axioms13040264 crossref_primary_10_1007_s11009_018_9648_x crossref_primary_10_1002_num_22254 crossref_primary_10_1016_j_camwa_2016_07_026 crossref_primary_10_1007_s10955_019_02475_1 crossref_primary_10_1016_j_camwa_2015_05_015 crossref_primary_10_1177_1077546314557554 crossref_primary_10_1007_s10915_019_01027_9 crossref_primary_10_1103_PhysRevE_84_066704 crossref_primary_10_1007_s11075_016_0169_9 crossref_primary_10_1007_s10955_011_0310_z crossref_primary_10_30757_ALEA_v21_59 crossref_primary_10_1088_1751_8121_aa9ad8 crossref_primary_10_1016_j_spl_2011_01_019 crossref_primary_10_4236_jamp_2024_124068 crossref_primary_10_1016_j_aml_2018_06_037 crossref_primary_10_1016_j_apnum_2016_10_011 crossref_primary_10_1186_s13662_019_1990_y crossref_primary_10_1007_s13540_023_00163_2 crossref_primary_10_2139_ssrn_4422376 crossref_primary_10_1029_2021WR031128 crossref_primary_10_1103_PhysRevE_99_062120 crossref_primary_10_1103_PhysRevE_84_061146 crossref_primary_10_3390_fractalfract9030187 crossref_primary_10_1016_j_physleta_2017_04_012 crossref_primary_10_1016_j_cma_2024_117448 crossref_primary_10_1214_16_ECP4383 crossref_primary_10_1007_s13540_021_00011_1 crossref_primary_10_1016_j_camwa_2016_12_017 crossref_primary_10_1103_PhysRevE_103_032133 crossref_primary_10_3934_math_20241318 crossref_primary_10_1155_2024_6710903 crossref_primary_10_1090_S0002_9939_2012_11362_0 crossref_primary_10_1016_j_cnsns_2023_107412 crossref_primary_10_1016_j_jde_2024_04_037 crossref_primary_10_1098_rsif_2016_0889 crossref_primary_10_1103_PhysRevE_84_021137 crossref_primary_10_1007_s11464_022_0185_0 crossref_primary_10_1515_ijcre_2024_0128 crossref_primary_10_1007_s10955_016_1547_3 crossref_primary_10_1016_j_physa_2012_05_072 crossref_primary_10_1016_j_physa_2016_07_041 crossref_primary_10_1007_s42967_020_00067_5 crossref_primary_10_1016_j_cam_2019_04_010 crossref_primary_10_1016_j_jhydrol_2019_124515 crossref_primary_10_2139_ssrn_2835371 crossref_primary_10_1103_PhysRevE_99_022122 crossref_primary_10_1515_fca_2021_0020 crossref_primary_10_3934_era_2024091 crossref_primary_10_1016_j_ress_2025_110818 crossref_primary_10_1088_1742_5468_2014_10_P10028 crossref_primary_10_1080_17442508_2017_1311897 crossref_primary_10_1007_s10444_016_9503_y crossref_primary_10_1016_j_chaos_2017_04_023 crossref_primary_10_1007_s10955_011_0191_1 crossref_primary_10_1016_j_bulsci_2024_103488 crossref_primary_10_1007_s10915_019_01029_7 crossref_primary_10_1103_PhysRevE_82_011117 crossref_primary_10_1016_j_amc_2019_124725 crossref_primary_10_1103_PhysRevE_92_012102 crossref_primary_10_1016_j_jcp_2014_05_026 crossref_primary_10_1016_j_cam_2024_115772 crossref_primary_10_1016_j_cnsns_2023_107118 crossref_primary_10_1186_s13662_017_1317_9 crossref_primary_10_1016_j_cnsns_2020_105178 crossref_primary_10_1002_fld_4901 crossref_primary_10_1007_s00180_024_01462_9 crossref_primary_10_4028_www_scientific_net_DDF_407_173 crossref_primary_10_1088_1742_5468_2013_10_P10011 crossref_primary_10_1016_j_jmaa_2020_124659 crossref_primary_10_2139_ssrn_3206896 crossref_primary_10_3934_dcdsb_2020319 crossref_primary_10_1137_140966083 crossref_primary_10_1016_j_padiff_2024_100938 crossref_primary_10_1007_s12190_019_01241_6 crossref_primary_10_1007_s10955_012_0537_3 crossref_primary_10_3390_jrfm14030136 crossref_primary_10_1063_1_4935475 crossref_primary_10_1142_S0218348X20500206 crossref_primary_10_2139_ssrn_1951537 crossref_primary_10_1007_s41478_023_00686_0 crossref_primary_10_1103_PhysRevE_82_011132 crossref_primary_10_1016_j_jhydrol_2020_125504 crossref_primary_10_1088_1751_8121_50_3_034002 crossref_primary_10_1016_j_physa_2016_09_018 crossref_primary_10_1007_s10915_019_00930_5 crossref_primary_10_1002_mma_4361 crossref_primary_10_1016_j_apnum_2017_05_012 crossref_primary_10_1007_s13160_016_0231_y crossref_primary_10_1029_2010GL043609 crossref_primary_10_1186_s13662_020_02594_0 crossref_primary_10_1016_j_aei_2024_102490 crossref_primary_10_1016_j_cam_2010_12_014 crossref_primary_10_1007_s42967_020_00080_8 crossref_primary_10_3390_fractalfract7030277 crossref_primary_10_1007_s10915_022_01835_6 crossref_primary_10_1016_j_spa_2014_03_002 crossref_primary_10_1007_s10915_018_0640_y crossref_primary_10_1080_00036811_2020_1751826 crossref_primary_10_1007_s10092_024_00604_1 crossref_primary_10_1017_S0021900200008925 crossref_primary_10_1002_mana_201700111 crossref_primary_10_1137_14097207X crossref_primary_10_1103_PhysRevE_93_032151 |
| Cites_doi | 10.3150/07-BEJ6011 10.1137/0517050 10.1016/S0370-1573(00)00070-3 10.1103/PhysRevE.76.041105 10.1103/PhysRevLett.73.2946 10.1007/s10955-006-9042-x 10.1016/j.cam.2004.01.033 10.1038/376046a0 10.1103/PhysRevE.59.5026 10.1088/0305-4470/37/31/R01 10.1103/PhysRevE.72.010101 10.1016/j.spa.2006.10.003 10.1016/S0895-7177(99)00105-3 10.1029/2008JF001246 10.1016/j.physa.2003.12.044 10.1239/jap/1091543414 10.1080/01621459.1976.10480344 10.1016/j.jcp.2005.08.008 |
| ContentType | Journal Article |
| Copyright | 2009 Elsevier B.V. 2015 INIST-CNRS |
| Copyright_xml | – notice: 2009 Elsevier B.V. – notice: 2015 INIST-CNRS |
| DBID | 6I. AAFTH AAYXX CITATION IQODW |
| DOI | 10.1016/j.cam.2009.10.027 |
| DatabaseName | ScienceDirect Open Access Titles Elsevier:ScienceDirect:Open Access CrossRef Pascal-Francis |
| DatabaseTitle | CrossRef |
| DatabaseTitleList | |
| DeliveryMethod | fulltext_linktorsrc |
| Discipline | Mathematics |
| EISSN | 1879-1778 |
| EndPage | 2448 |
| ExternalDocumentID | 22540404 10_1016_j_cam_2009_10_027 S0377042709007250 |
| GroupedDBID | --K --M -~X .~1 0R~ 1B1 1RT 1~. 1~5 29K 4.4 457 4G. 5GY 5VS 6I. 7-5 71M 8P~ 9JN AABNK AACTN AAEDT AAEDW AAFTH AAFWJ AAIAV AAIKJ AAKOC AALRI AAOAW AAQFI AAQXK AAXUO ABAOU ABEFU ABFNM ABJNI ABMAC ABTAH ABVKL ABXDB ABYKQ ACAZW ACDAQ ACGFS ACRLP ADBBV ADEZE ADMUD AEBSH AEKER AENEX AEXQZ AFKWA AFTJW AGHFR AGUBO AGYEJ AHHHB AIEXJ AIGVJ AIKHN AITUG AJBFU AJOXV ALMA_UNASSIGNED_HOLDINGS AMFUW AMRAJ ARUGR ASPBG AVWKF AXJTR AZFZN BKOJK BLXMC CS3 D-I DU5 EBS EFJIC EFLBG EJD EO8 EO9 EP2 EP3 F5P FDB FEDTE FGOYB FIRID FNPLU FYGXN G-2 G-Q G8K GBLVA HVGLF HZ~ IHE IXB J1W KOM LG9 M26 M41 MHUIS MO0 N9A NCXOZ NHB O-L O9- OAUVE OK1 OZT P-8 P-9 P2P PC. Q38 R2- RIG RNS ROL RPZ SDF SDG SDP SES SEW SPC SPCBC SSW SSZ T5K TN5 UPT WUQ XPP YQT ZMT ZY4 ~02 ~G- AATTM AAXKI AAYWO AAYXX ABDPE ABWVN ACLOT ACRPL ACVFH ADCNI ADNMO ADVLN AEIPS AEUPX AFJKZ AFPUW AGQPQ AIGII AIIUN AKBMS AKRWK AKYEP ANKPU APXCP CITATION EFKBS ~HD AFXIZ AGCQF AGRNS BNPGV IQODW SSH |
| ID | FETCH-LOGICAL-c327t-26aa5ab2906b3d31d05d647354d44c25c14c053d72e9a14ce2f86a2bb33c11193 |
| IEDL.DBID | AIKHN |
| ISSN | 0377-0427 |
| IngestDate | Mon Jul 21 09:14:07 EDT 2025 Wed Oct 01 04:36:53 EDT 2025 Thu Apr 24 23:09:00 EDT 2025 Fri Feb 23 02:27:51 EST 2024 |
| IsDoiOpenAccess | true |
| IsOpenAccess | true |
| IsPeerReviewed | true |
| IsScholarly | true |
| Issue | 10 |
| Keywords | Fractional derivatives Particle tracking Power law Truncated power law Numerical analysis Applied mathematics Crank Nicolson method Diffusion equation Finite difference method |
| Language | English |
| License | http://www.elsevier.com/open-access/userlicense/1.0 https://www.elsevier.com/tdm/userlicense/1.0 https://www.elsevier.com/open-access/userlicense/1.0 CC BY 4.0 |
| LinkModel | DirectLink |
| MergedId | FETCHMERGED-LOGICAL-c327t-26aa5ab2906b3d31d05d647354d44c25c14c053d72e9a14ce2f86a2bb33c11193 |
| OpenAccessLink | https://www.sciencedirect.com/science/article/pii/S0377042709007250 |
| PageCount | 11 |
| ParticipantIDs | pascalfrancis_primary_22540404 crossref_primary_10_1016_j_cam_2009_10_027 crossref_citationtrail_10_1016_j_cam_2009_10_027 elsevier_sciencedirect_doi_10_1016_j_cam_2009_10_027 |
| ProviderPackageCode | CITATION AAYXX |
| PublicationCentury | 2000 |
| PublicationDate | 2010-03-15 |
| PublicationDateYYYYMMDD | 2010-03-15 |
| PublicationDate_xml | – month: 03 year: 2010 text: 2010-03-15 day: 15 |
| PublicationDecade | 2010 |
| PublicationPlace | Kidlington |
| PublicationPlace_xml | – name: Kidlington |
| PublicationTitle | Journal of computational and applied mathematics |
| PublicationYear | 2010 |
| Publisher | Elsevier B.V Elsevier |
| Publisher_xml | – name: Elsevier B.V – name: Elsevier |
| References | R. Schumer, M.M. Meerschaert, B. Baeumer, Fractional advection-dispersion equations for modeling transport at the Earth surface, J. Geophys. Res. (2009) in press Preprint available at Chambers, Mallows, Stuck (b26) 1976; 71 Cohen, Rosiński (b28) 2007; 13 Metzler, Klafter (b2) 2000; 339 (b6) 1995 Mantegna, Stanley (b10) 1994; 73 Sokolov, Chechkin, Klafter (b12) 2004; 336 Zhang, Benson, Meerschaert, Scheffler (b18) 2006; 123 Lubich (b24) 1986; 17 Meerschaert, Scheffler (b7) 2004; 41 E. Scalas, Five years of Continuous-Time Random Walks in Econophysics. in: A. Namatame (Ed.), Proceedings of WEHIA 2004, Kyoto, 2004 Widder (b23) 1946; vol. 6 Rosiński (b14) 2007; 117 Zolotarev (b20) 1986; vol. 65 Tadjeran, Meerschaert, Scheffler (b17) 2006; 213 Feller (b4) 1971 Mantegna, Stanley (b11) 1995; 376 Meerschaert, Benson, Bäumer (b1) 1999; 59 Butzer, Nessel (b22) 1971; vol. 40 Samorodnitsky, Taqqu (b19) 1994 Metzler, Klafter (b3) 2004; 37 Chechkin, Gonchar, Klafter, Metzler (b13) 2005; 72 Isaacson, Keller (b25) 1966 Nikias, Shao (b5) 1995 Meerschaert, Tadjeran (b16) 2004; 172 Meerschaert, Scheffler (b21) 2001 Nolan (b27) 1999; 29 Cartea, del Castillo-Negrete (b15) 2007; 76 10.1016/j.cam.2009.10.027_b9 (10.1016/j.cam.2009.10.027_b6) 1995 Meerschaert (10.1016/j.cam.2009.10.027_b1) 1999; 59 Lubich (10.1016/j.cam.2009.10.027_b24) 1986; 17 Zolotarev (10.1016/j.cam.2009.10.027_b20) 1986; vol. 65 10.1016/j.cam.2009.10.027_b8 Chambers (10.1016/j.cam.2009.10.027_b26) 1976; 71 Feller (10.1016/j.cam.2009.10.027_b4) 1971 Isaacson (10.1016/j.cam.2009.10.027_b25) 1966 Cohen (10.1016/j.cam.2009.10.027_b28) 2007; 13 Zhang (10.1016/j.cam.2009.10.027_b18) 2006; 123 Widder (10.1016/j.cam.2009.10.027_b23) 1946; vol. 6 Metzler (10.1016/j.cam.2009.10.027_b3) 2004; 37 Mantegna (10.1016/j.cam.2009.10.027_b11) 1995; 376 Butzer (10.1016/j.cam.2009.10.027_b22) 1971; vol. 40 Chechkin (10.1016/j.cam.2009.10.027_b13) 2005; 72 Sokolov (10.1016/j.cam.2009.10.027_b12) 2004; 336 Samorodnitsky (10.1016/j.cam.2009.10.027_b19) 1994 Meerschaert (10.1016/j.cam.2009.10.027_b21) 2001 Meerschaert (10.1016/j.cam.2009.10.027_b16) 2004; 172 Meerschaert (10.1016/j.cam.2009.10.027_b7) 2004; 41 Nolan (10.1016/j.cam.2009.10.027_b27) 1999; 29 Rosiński (10.1016/j.cam.2009.10.027_b14) 2007; 117 Metzler (10.1016/j.cam.2009.10.027_b2) 2000; 339 Cartea (10.1016/j.cam.2009.10.027_b15) 2007; 76 Nikias (10.1016/j.cam.2009.10.027_b5) 1995 Mantegna (10.1016/j.cam.2009.10.027_b10) 1994; 73 Tadjeran (10.1016/j.cam.2009.10.027_b17) 2006; 213 |
| References_xml | – year: 1971 ident: b4 article-title: An Introduction to Probability Theory and Its Applications, Vol. II – volume: vol. 40 year: 1971 ident: b22 article-title: Fourier analysis and approximation publication-title: Volume 1: One-dimensional Theory – year: 1995 ident: b6 publication-title: Lévy Flights and Related Topics in Physics – volume: 172 start-page: 65 year: 2004 end-page: 77 ident: b16 article-title: Finite difference approximations for fractional advection-dispersion flow equations publication-title: J. Comput. Appl. Math. – volume: 71 start-page: 340 year: 1976 end-page: 344 ident: b26 article-title: A method for simulating stable random variables publication-title: J. Amer. Statist. Assoc. – reference: ). Preprint available at: – volume: 73 start-page: 2946 year: 1994 end-page: 2949 ident: b10 article-title: Stochastic process with ultraslow convergence to a Gaussian: The truncated Lévy flight publication-title: Phys. Rev. Lett. – year: 1994 ident: b19 article-title: Stable Non-Gaussian Random Processes – volume: vol. 65 year: 1986 ident: b20 article-title: One-dimensional stable distributions publication-title: Translations of Mathematical Monographs – volume: 376 start-page: 46 year: 1995 end-page: 49 ident: b11 article-title: Scaling behavior in the dyamics of an economic index publication-title: Nature – volume: 339 start-page: 1 year: 2000 end-page: 77 ident: b2 article-title: The random walk’s guide to anomalous diffusion: A fractional dynamics approach publication-title: Phys. Rep. – volume: 17 start-page: 704 year: 1986 end-page: 719 ident: b24 article-title: Discretized fractional calculus publication-title: SIAM J. Math. Anal. – volume: 76 start-page: 041105 year: 2007 ident: b15 article-title: Fluid limit of the continuous-time random walk with general Lévy jump distribution functions publication-title: Phys. Rev. E – volume: 59 start-page: 5026 year: 1999 end-page: 5028 ident: b1 article-title: Multidimensional advection and fractional dispersion publication-title: Phys. Rev. E – volume: 29 start-page: 229 year: 1999 end-page: 233 ident: b27 article-title: An algorithm for evaluating stable densities in Zolotarev’s (M) parameterization publication-title: Math. Comput. Modeling – volume: 37 start-page: R161 year: 2004 end-page: R208 ident: b3 article-title: The restaurant at the end of the random walk: Recent developments in the description of anomalous transport by fractional dynamics publication-title: J. Phys. A – volume: 72 start-page: 010101 year: 2005 ident: b13 article-title: Natural cutoff in Lévy flights caused by dissipative nonlinearity publication-title: Phys. Rev. E – volume: vol. 6 year: 1946 ident: b23 publication-title: The Laplace Transform – volume: 13 start-page: 195 year: 2007 end-page: 210 ident: b28 article-title: Gaussian approximation of multivariate Lévy processes with applications to simulation of tempered stable processes publication-title: Bernoulli – volume: 123 start-page: 89 year: 2006 end-page: 110 ident: b18 article-title: On using random walks to solve the space-fractional advection-dispersion equations publication-title: J. Statist. Phys. – reference: E. Scalas, Five years of Continuous-Time Random Walks in Econophysics. in: A. Namatame (Ed.), Proceedings of WEHIA 2004, Kyoto, 2004 – volume: 117 start-page: 677 year: 2007 end-page: 707 ident: b14 article-title: Tempering stable processes publication-title: Stochastic Process. Appl. – year: 2001 ident: b21 article-title: Limit Distributions for Sums of Independent Random Vectors: Heavy Tails in Theory and Practice – volume: 41 start-page: 623 year: 2004 end-page: 638 ident: b7 article-title: Limit theorems for continuous time random walks with infinite mean waiting times publication-title: J. Appl. Probab. – volume: 336 start-page: 245 year: 2004 end-page: 251 ident: b12 article-title: Fractional diffusion equation for a power-law-truncated Lévy process publication-title: Physica A – reference: R. Schumer, M.M. Meerschaert, B. Baeumer, Fractional advection-dispersion equations for modeling transport at the Earth surface, J. Geophys. Res. (2009) in press ( – year: 1966 ident: b25 article-title: Analysis of Numerical Methods – volume: 213 start-page: 205 year: 2006 end-page: 213 ident: b17 article-title: A second-order accurate numerical approximation for the fractional diffusion equation publication-title: J. Comput. Phys. – year: 1995 ident: b5 article-title: Signal Processing with Alpha Stable Distributions and Applications – volume: 13 start-page: 195 year: 2007 ident: 10.1016/j.cam.2009.10.027_b28 article-title: Gaussian approximation of multivariate Lévy processes with applications to simulation of tempered stable processes publication-title: Bernoulli doi: 10.3150/07-BEJ6011 – volume: 17 start-page: 704 year: 1986 ident: 10.1016/j.cam.2009.10.027_b24 article-title: Discretized fractional calculus publication-title: SIAM J. Math. Anal. doi: 10.1137/0517050 – volume: 339 start-page: 1 year: 2000 ident: 10.1016/j.cam.2009.10.027_b2 article-title: The random walk’s guide to anomalous diffusion: A fractional dynamics approach publication-title: Phys. Rep. doi: 10.1016/S0370-1573(00)00070-3 – volume: 76 start-page: 041105 year: 2007 ident: 10.1016/j.cam.2009.10.027_b15 article-title: Fluid limit of the continuous-time random walk with general Lévy jump distribution functions publication-title: Phys. Rev. E doi: 10.1103/PhysRevE.76.041105 – year: 1966 ident: 10.1016/j.cam.2009.10.027_b25 – ident: 10.1016/j.cam.2009.10.027_b8 – volume: 73 start-page: 2946 year: 1994 ident: 10.1016/j.cam.2009.10.027_b10 article-title: Stochastic process with ultraslow convergence to a Gaussian: The truncated Lévy flight publication-title: Phys. Rev. Lett. doi: 10.1103/PhysRevLett.73.2946 – volume: vol. 40 year: 1971 ident: 10.1016/j.cam.2009.10.027_b22 article-title: Fourier analysis and approximation – volume: 123 start-page: 89 year: 2006 ident: 10.1016/j.cam.2009.10.027_b18 article-title: On using random walks to solve the space-fractional advection-dispersion equations publication-title: J. Statist. Phys. doi: 10.1007/s10955-006-9042-x – volume: vol. 65 year: 1986 ident: 10.1016/j.cam.2009.10.027_b20 article-title: One-dimensional stable distributions – volume: 172 start-page: 65 year: 2004 ident: 10.1016/j.cam.2009.10.027_b16 article-title: Finite difference approximations for fractional advection-dispersion flow equations publication-title: J. Comput. Appl. Math. doi: 10.1016/j.cam.2004.01.033 – year: 1971 ident: 10.1016/j.cam.2009.10.027_b4 – volume: 376 start-page: 46 year: 1995 ident: 10.1016/j.cam.2009.10.027_b11 article-title: Scaling behavior in the dyamics of an economic index publication-title: Nature doi: 10.1038/376046a0 – year: 1994 ident: 10.1016/j.cam.2009.10.027_b19 – volume: 59 start-page: 5026 year: 1999 ident: 10.1016/j.cam.2009.10.027_b1 article-title: Multidimensional advection and fractional dispersion publication-title: Phys. Rev. E doi: 10.1103/PhysRevE.59.5026 – volume: 37 start-page: R161 year: 2004 ident: 10.1016/j.cam.2009.10.027_b3 article-title: The restaurant at the end of the random walk: Recent developments in the description of anomalous transport by fractional dynamics publication-title: J. Phys. A doi: 10.1088/0305-4470/37/31/R01 – year: 1995 ident: 10.1016/j.cam.2009.10.027_b6 – volume: 72 start-page: 010101 year: 2005 ident: 10.1016/j.cam.2009.10.027_b13 article-title: Natural cutoff in Lévy flights caused by dissipative nonlinearity publication-title: Phys. Rev. E doi: 10.1103/PhysRevE.72.010101 – volume: 117 start-page: 677 year: 2007 ident: 10.1016/j.cam.2009.10.027_b14 article-title: Tempering stable processes publication-title: Stochastic Process. Appl. doi: 10.1016/j.spa.2006.10.003 – volume: 29 start-page: 229 year: 1999 ident: 10.1016/j.cam.2009.10.027_b27 article-title: An algorithm for evaluating stable densities in Zolotarev’s (M) parameterization publication-title: Math. Comput. Modeling doi: 10.1016/S0895-7177(99)00105-3 – year: 1995 ident: 10.1016/j.cam.2009.10.027_b5 – year: 2001 ident: 10.1016/j.cam.2009.10.027_b21 – ident: 10.1016/j.cam.2009.10.027_b9 doi: 10.1029/2008JF001246 – volume: 336 start-page: 245 year: 2004 ident: 10.1016/j.cam.2009.10.027_b12 article-title: Fractional diffusion equation for a power-law-truncated Lévy process publication-title: Physica A doi: 10.1016/j.physa.2003.12.044 – volume: 41 start-page: 623 year: 2004 ident: 10.1016/j.cam.2009.10.027_b7 article-title: Limit theorems for continuous time random walks with infinite mean waiting times publication-title: J. Appl. Probab. doi: 10.1239/jap/1091543414 – volume: vol. 6 year: 1946 ident: 10.1016/j.cam.2009.10.027_b23 – volume: 71 start-page: 340 year: 1976 ident: 10.1016/j.cam.2009.10.027_b26 article-title: A method for simulating stable random variables publication-title: J. Amer. Statist. Assoc. doi: 10.1080/01621459.1976.10480344 – volume: 213 start-page: 205 year: 2006 ident: 10.1016/j.cam.2009.10.027_b17 article-title: A second-order accurate numerical approximation for the fractional diffusion equation publication-title: J. Comput. Phys. doi: 10.1016/j.jcp.2005.08.008 |
| SSID | ssj0006914 |
| Score | 2.4423351 |
| Snippet | The space-fractional diffusion equation models anomalous super-diffusion. Its solutions are transition densities of a stable Lévy motion, representing the... |
| SourceID | pascalfrancis crossref elsevier |
| SourceType | Index Database Enrichment Source Publisher |
| StartPage | 2438 |
| SubjectTerms | Exact sciences and technology Fractional derivatives Mathematical analysis Mathematics Numerical analysis Numerical analysis. Scientific computation Particle tracking Power law Real functions Sciences and techniques of general use Truncated power law |
| Title | Tempered stable Lévy motion and transient super-diffusion |
| URI | https://dx.doi.org/10.1016/j.cam.2009.10.027 |
| Volume | 233 |
| hasFullText | 1 |
| inHoldings | 1 |
| isFullTextHit | |
| isPrint | |
| journalDatabaseRights | – providerCode: PRVESC databaseName: Elsevier Free Content customDbUrl: eissn: 1879-1778 dateEnd: 20211105 omitProxy: true ssIdentifier: ssj0006914 issn: 0377-0427 databaseCode: IXB dateStart: 19750301 isFulltext: true titleUrlDefault: https://www.sciencedirect.com providerName: Elsevier – providerCode: PRVESC databaseName: Elsevier SD Complete Freedom Collection [SCCMFC] customDbUrl: eissn: 1879-1778 dateEnd: 20211105 omitProxy: true ssIdentifier: ssj0006914 issn: 0377-0427 databaseCode: ACRLP dateStart: 19950220 isFulltext: true titleUrlDefault: https://www.sciencedirect.com providerName: Elsevier – providerCode: PRVESC databaseName: Elsevier SD Freedom Collection customDbUrl: eissn: 1879-1778 dateEnd: 20211015 omitProxy: true ssIdentifier: ssj0006914 issn: 0377-0427 databaseCode: AIKHN dateStart: 19950220 isFulltext: true titleUrlDefault: https://www.sciencedirect.com providerName: Elsevier – providerCode: PRVESC databaseName: Elsevier SD Freedom Collection customDbUrl: eissn: 1879-1778 dateEnd: 99991231 omitProxy: true ssIdentifier: ssj0006914 issn: 0377-0427 databaseCode: .~1 dateStart: 19950101 isFulltext: true titleUrlDefault: https://www.sciencedirect.com providerName: Elsevier – providerCode: PRVLSH databaseName: Elsevier Journals customDbUrl: mediaType: online eissn: 1879-1778 dateEnd: 99991231 omitProxy: true ssIdentifier: ssj0006914 issn: 0377-0427 databaseCode: AKRWK dateStart: 19750301 isFulltext: true providerName: Library Specific Holdings |
| link | http://utb.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwnV1LS8NAEF5qe1FEfOKz5OBJWJtkN5vEWy1Kq7YXW-gt7CugaC19CF78P_4O_5gzeRQL0oO3ZNlNwrfJN7PZmfkIOU_RKEUypNJPs5SciCoVcqoE06lSwjVZUli3J9oDfjcMhhXSKnNhMKyy4P6c0zO2LloaBZqN8dNT49FlYYhKEW6M5a9x3V4D-xNFVVJrdu7bvQUhizgv8Q39KQ4oNzezMC8tX_OqlRjjhdoyf5unzbGcAmhprnbxywTdbpOtwnd0mvnj7ZCKHe2Sje6i8Op0j1z1LfjBE2sc8PrUi3Uevr_eP5xcq8eRI-PM0DhhEqQznUNPigopc_xltk8Gtzf9VpsW8ghUMz-cUV9IGUiF9doVM8wzbmAEKglzw7n2A-1xDZ-YCX0bSzi2fhoJ6SvFmAaGi9kBqY7eRvaQOAb9NuvhFqrmgFCsRGo8N3W1kAocuiPilqgkuqgdjhIWL0kZJPacAJCoaRljEwB5RC4WQ8Z54YxVnXkJdbI0-wkQ-6ph9aVpWdwISIoDO_Hj_133hKznQQKMesEpqc4mc3sGvsdM1cna5adXL94wOOsMr38A_XnX7g |
| linkProvider | Elsevier |
| linkToHtml | http://utb.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwnV1LS8NAEF5KPaiI-MT6qDl4EtYm2c2m8SbFUrXtxRZ6C_sKVGosbSp48f_4O_xj7mSTakE8eAvLbBK-TWYm2ZnvQ-gigaDU5CHmfpK35DSxECHFghGZCMFclTeF9fqsM6T3o2BUQa2yFwbKKgvfb3167q2LkUaBZmM6HjceXRKGoBThRkB_Dd_tazTwQ_gCu3r_rvNgkSX4NtYYzMutzbzIS_Jny1kJFV6gLPN7cNqa8rmBLLFaFz8CUHsHbReZo3Njb24XVXS6hzZ7S9rV-T66HmiTBc-0ckzOJyba6X5-vL45VqnH4alyMghN0ALpzBfGEoM-ygJ-mB2gYft20OrgQhwBS-KHGfYZ5wEXwNYuiCKecgPFQEeYKkqlH0iPSvOCqdDXETfH2k-ajPtCECKNf4vIIaqmL6k-Qo6CrE17sIEqqUEoEixRnpu4knFh0rkacktUYlkwh4OAxSQuS8SeYgMkKFpGMGSArKHL5ZSppc34y5iWUMcrax8bt_7XtPrKsiwvZFwUNb6JHv_vvOdovTPodePuXf_hBG3YcgGCveAUVbPZQp-ZLCQT9fwp-wK0ddey |
| openUrl | ctx_ver=Z39.88-2004&ctx_enc=info%3Aofi%2Fenc%3AUTF-8&rfr_id=info%3Asid%2Fsummon.serialssolutions.com&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.atitle=Tempered+stable+L%C3%A9vy+motion+and+transient+super-diffusion&rft.jtitle=Journal+of+computational+and+applied+mathematics&rft.au=Baeumer%2C+Boris&rft.au=Meerschaert%2C+Mark+M.&rft.date=2010-03-15&rft.issn=0377-0427&rft.volume=233&rft.issue=10&rft.spage=2438&rft.epage=2448&rft_id=info:doi/10.1016%2Fj.cam.2009.10.027&rft.externalDBID=n%2Fa&rft.externalDocID=10_1016_j_cam_2009_10_027 |
| thumbnail_l | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/lc.gif&issn=0377-0427&client=summon |
| thumbnail_m | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/mc.gif&issn=0377-0427&client=summon |
| thumbnail_s | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/sc.gif&issn=0377-0427&client=summon |