Unified representation of formulas for single birth processes
Based on a new explicit representation of the solution to the Poisson equation with respect to single birth processes, the unified treatment for various criteria on classical problems (including uniqueness, recurrence, ergodicity, exponential ergodicity, strong ergodicity, as well as extinction prob...
Saved in:
| Published in | Frontiers of Mathematics Vol. 9; no. 4; pp. 761 - 796 |
|---|---|
| Main Authors | , |
| Format | Journal Article |
| Language | English |
| Published |
Heidelberg
Higher Education Press
01.08.2014
Springer Nature B.V |
| Subjects | |
| Online Access | Get full text |
| ISSN | 1673-3452 2731-8648 1673-3576 2731-8656 |
| DOI | 10.1007/s11464-014-0381-7 |
Cover
| Abstract | Based on a new explicit representation of the solution to the Poisson equation with respect to single birth processes, the unified treatment for various criteria on classical problems (including uniqueness, recurrence, ergodicity, exponential ergodicity, strong ergodicity, as well as extinction probability, etc.) for the processes are presented. |
|---|---|
| AbstractList | Based on a new explicit representation of the solution to the Poisson equation with respect to single birth processes, the unified treatment for various criteria on classical problems （including uniqueness, recurrence, ergodicity, exponential ergodicity, strong ergodicity, as well as extinction probability, etc.） for the processes are presented. Based on a new explicit representation of the solution to the Poisson equation with respect to single birth processes, the unified treatment for various criteria on classical problems (including uniqueness, recurrence, ergodicity, exponential ergodicity, strong ergodicity, as well as extinction probability, etc.) for the processes are presented. Issue Title: Markov Processes and Related Topics Based on a new explicit representation of the solution to the Poisson equation with respect to single birth processes, the unified treatment for various criteria on classical problems (including uniqueness, recurrence, ergodicity, exponential ergodicity, strong ergodicity, as well as extinction probability, etc.) for the processes are presented.[PUBLICATION ABSTRACT] |
| Author | Mu-Fa CHEN Yuhui ZHANG |
| AuthorAffiliation | School of Mathematical Sciences, Beijing Normal University, Laboratory of Mathematics andComplex Systems, Ministry of Education, Beijing 100875, China |
| Author_xml | – sequence: 1 givenname: Mu-Fa surname: CHEN fullname: CHEN, Mu-Fa organization: School of Mathematical Sciences, Beijing Normal University, Laboratory of Mathematics and Complex Systems, Ministry of Education, Beijing 100875, China – sequence: 2 givenname: Yuhui surname: ZHANG fullname: ZHANG, Yuhui email: zhangyh@bnu.edu.cn organization: School of Mathematical Sciences, Beijing Normal University, Laboratory of Mathematics and Complex Systems, Ministry of Education, Beijing 100875, China |
| BookMark | eNp9kb1uFDEURq0oSCSBB6AbQUMz4Dv-mykoUJQEpEg0obY8nutdR7P2xne24O3xahKEUmxh-Rbn2J8_X7LzlBMy9gH4F-DcfCUAqWXLoS7RQ2vO2AVoI1qhjD5_maXq3rJLokfOFWg1XLBvv1MMEaem4L4gYVrcEnNqcmhCLrvD7Og4NBTTZsZmjGXZNvuSPRIhvWNvgpsJ3z_vV-zh9ubh-kd7_-vu5_X3-9ZL1S-tEGFUQo1-CsjlyIfBaWVAKcOnznk5Kqd77voACvw4iuD8aHBwMHXCDJ24Yp_XY-vFTwekxe4ieZxnlzAfyILSBrg2Ulf00yv0MR9KquEqpbjsRQeyUmalfMlEBYP1cX34UlycLXB7bNWurdraqj22ak014ZW5L3Hnyp-TTrc6VNm0wfJfphNSv0rbuNliwen4PWRDqRkjltPqx-eM25w2T_XKfyG17rgWQg3iL9qDqIw |
| CitedBy_id | crossref_primary_10_1007_s40304_014_0028_8 crossref_primary_10_1016_j_jmaa_2021_125483 crossref_primary_10_1137_22M1489861 crossref_primary_10_1007_s11464_018_0722_z crossref_primary_10_1007_s10959_021_01105_5 crossref_primary_10_1360_SCM_2022_0745 crossref_primary_10_1007_s10959_018_0820_6 crossref_primary_10_1016_j_amc_2021_126610 crossref_primary_10_1007_s11464_016_0573_4 crossref_primary_10_1007_s11464_021_0898_5 crossref_primary_10_1016_j_spl_2024_110120 crossref_primary_10_1007_s40304_014_0041_y crossref_primary_10_1016_j_jmaa_2020_124919 |
| Cites_doi | 10.1007/s11464-010-0068-7 10.1239/jap/996986662 10.1142/S0252959999000114 10.1239/jap/1101840548 10.1142/5513 10.2307/1427020 10.1007/978-1-4612-3038-0 10.1360/02ys0306 10.2307/3214459 10.1016/j.jmaa.2005.04.068 |
| ContentType | Journal Article |
| Copyright | Copyright reserved, 2014, Higher Education Press and Springer-Verlag Berlin Heidelberg Higher Education Press and Springer-Verlag Berlin Heidelberg 2014 |
| Copyright_xml | – notice: Copyright reserved, 2014, Higher Education Press and Springer-Verlag Berlin Heidelberg – notice: Higher Education Press and Springer-Verlag Berlin Heidelberg 2014 |
| DBID | 2RA 92L CQIGP W92 ~WA AAYXX CITATION 3V. 7SC 7TB 7WY 7WZ 7XB 87Z 88I 8AL 8FD 8FE 8FG 8FK 8FL ABJCF ABUWG AFKRA ARAPS AZQEC BENPR BEZIV BGLVJ CCPQU DWQXO FR3 FRNLG F~G GNUQQ HCIFZ JQ2 K60 K6~ K7- KR7 L.- L.0 L6V L7M L~C L~D M0C M0N M2P M7S P5Z P62 PHGZM PHGZT PKEHL PQBIZ PQBZA PQEST PQGLB PQQKQ PQUKI PRINS PTHSS PYYUZ Q9U |
| DOI | 10.1007/s11464-014-0381-7 |
| DatabaseName | 维普期刊资源整合服务平台 中文科技期刊数据库-CALIS站点 维普中文期刊数据库 中文科技期刊数据库-工程技术 中文科技期刊数据库- 镜像站点 CrossRef ProQuest Central (Corporate) Computer and Information Systems Abstracts Mechanical & Transportation Engineering Abstracts ABI/INFORM Collection ABI/INFORM Global (PDF only) ProQuest Central (purchase pre-March 2016) ABI/INFORM Collection Science Database (Alumni Edition) Computing Database (Alumni Edition) Technology Research Database ProQuest SciTech Collection ProQuest Technology Collection ProQuest Central (Alumni) (purchase pre-March 2016) ABI/INFORM Collection (Alumni) Materials Science & Engineering Collection ProQuest Central (Alumni) ProQuest Central UK/Ireland ProQuest Advanced Technologies & Aerospace Database ProQuest Central Essentials ProQuest Central Business Premium Collection ProQuest Technology Collection ProQuest One Community College ProQuest Central Korea Engineering Research Database Business Premium Collection (Alumni) ABI/INFORM Global (Corporate) ProQuest Central Student SciTech Premium Collection ProQuest Computer Science Collection ProQuest Business Collection (Alumni Edition) ProQuest Business Collection Computer Science Database Civil Engineering Abstracts ABI/INFORM Professional Advanced ABI/INFORM Professional Standard ProQuest Engineering Collection Advanced Technologies Database with Aerospace Computer and Information Systems Abstracts Academic Computer and Information Systems Abstracts Professional ABI/INFORM Global Computing Database Science Database Engineering Database Advanced Technologies & Aerospace Database ProQuest Advanced Technologies & Aerospace Collection ProQuest Central Premium ProQuest One Academic (New) ProQuest One Academic Middle East (New) ProQuest One Business ProQuest One Business (Alumni) ProQuest One Academic Eastern Edition (DO NOT USE) ProQuest One Applied & Life Sciences ProQuest One Academic ProQuest One Academic UKI Edition ProQuest Central China Engineering Collection ABI/INFORM Collection China ProQuest Central Basic |
| DatabaseTitle | CrossRef ProQuest Business Collection (Alumni Edition) Computer Science Database ProQuest Central Student ProQuest Advanced Technologies & Aerospace Collection ProQuest Central Essentials ProQuest Computer Science Collection Computer and Information Systems Abstracts SciTech Premium Collection ProQuest Central China ABI/INFORM Complete ProQuest One Applied & Life Sciences ProQuest Central (New) Engineering Collection Advanced Technologies & Aerospace Collection Business Premium Collection ABI/INFORM Global Engineering Database ProQuest Science Journals (Alumni Edition) ProQuest One Academic Eastern Edition ProQuest Technology Collection ProQuest Business Collection ProQuest One Academic UKI Edition Engineering Research Database ProQuest One Academic ProQuest One Academic (New) ABI/INFORM Global (Corporate) ProQuest One Business Technology Collection Technology Research Database Computer and Information Systems Abstracts – Academic ProQuest One Academic Middle East (New) Mechanical & Transportation Engineering Abstracts ProQuest Central (Alumni Edition) ProQuest One Community College ProQuest Central ABI/INFORM Professional Advanced ProQuest Engineering Collection ABI/INFORM Professional Standard ProQuest Central Korea Advanced Technologies Database with Aerospace ABI/INFORM Complete (Alumni Edition) Civil Engineering Abstracts ProQuest Computing ABI/INFORM Global (Alumni Edition) ProQuest Central Basic ProQuest Science Journals ProQuest Computing (Alumni Edition) ABI/INFORM China ProQuest SciTech Collection Computer and Information Systems Abstracts Professional Advanced Technologies & Aerospace Database Materials Science & Engineering Collection ProQuest One Business (Alumni) ProQuest Central (Alumni) Business Premium Collection (Alumni) |
| DatabaseTitleList | Civil Engineering Abstracts ProQuest Business Collection (Alumni Edition) |
| Database_xml | – sequence: 1 dbid: 8FG name: ProQuest Technology Collection url: https://search.proquest.com/technologycollection1 sourceTypes: Aggregation Database |
| DeliveryMethod | fulltext_linktorsrc |
| Discipline | Mathematics |
| DocumentTitleAlternate | Unified representation of formulas for single birth processes |
| EISSN | 1673-3576 2731-8656 |
| EndPage | 796 |
| ExternalDocumentID | 3390470971 10_1007_s11464_014_0381_7 10.1007/s11464-014-0381-7 662063359 |
| Genre | Feature |
| GroupedDBID | -5D -5G -BR -EM -Y2 -~C .VR 06D 0R~ 0VY 1-T 1N0 2J2 2JN 2JY 2KG 2KM 2LR 2RA 2VQ 2~H 30V 3V. 4.4 408 40D 40E 5VS 6NX 7WY 88I 8FE 8FG 8FL 8TC 92L 95- 95. 95~ 96X AAAVM AABHQ AAFGU AAIAL AAJKR AANZL AARHV AARTL AATVU AAUYE AAWCG AAYFA AAYIU AAYQN AAYTO ABBBX ABDBF ABDZT ABECU ABFGW ABFTV ABHQN ABJCF ABJNI ABJOX ABKAS ABKCH ABKTR ABMNI ABMQK ABNWP ABQBU ABSXP ABTEG ABTHY ABTKH ABTMW ABUWG ABWNU ABXPI ACBMV ACBRV ACBXY ACGFS ACGOD ACHSB ACHXU ACIPQ ACIWK ACKNC ACMDZ ACMLO ACOKC ACOMO ACSNA ACTTH ACVWB ACWMK ADHHG ADHIR ADINQ ADKNI ADKPE ADMDM ADRFC ADTPH ADURQ ADYFF ADZKW AEBTG AEFTE AEGAL AEGNC AEJHL AEJRE AEKMD AENEX AEOHA AEPYU AESTI AETLH AEVLU AEVTX AEXYK AFGCZ AFKRA AFLOW AFQWF AFWTZ AFZKB AGAYW AGDGC AGGBP AGJBK AGMZJ AGQMX AGWIL AGWZB AGYKE AHAVH AHBYD AHKAY AHSBF AHYZX AIAKS AIIXL AILAN AIMYW AITGF AJBLW AJDOV AJRNO ALMA_UNASSIGNED_HOLDINGS ALWAN AMKLP AMXSW AMYLF AMYQR AOCGG ARAPS ARMRJ ASPBG AVWKF AXYYD AZFZN AZQEC B-. BA0 BAPOH BDATZ BENPR BEZIV BGLVJ BGNMA BPHCQ CAG CCPQU COF CQIGP CS3 CSCUP DNIVK DU5 DWQXO EBLON EBS EIOEI EJD ESBYG FEDTE FERAY FFXSO FIGPU FINBP FNLPD FRNLG FRRFC FSGXE FWDCC GGCAI GGRSB GJIRD GNUQQ GNWQR GQ6 GQ7 GROUPED_ABI_INFORM_COMPLETE HCIFZ HF~ HG6 HLICF HMJXF HRMNR HVGLF HZ~ IHE IJ- IKXTQ IWAJR IXD I~X I~Z J-C J9A JBSCW K60 K6V K6~ K7- KOV L6V LLZTM M0C M0N M2P M4Y M7S MA- N2Q NQJWS NU0 O9- O9J P2P P4S P62 P9R PF0 PQBIZ PQQKQ PROAC PT4 PTHSS Q2X QOS R89 R9I ROL RPX RSV S16 S1Z S27 S3B SAP SCL SDH SHX SISQX SMT SNE SNPRN SNX SOHCF SOJ SPISZ SRMVM SSLCW STPWE SZN T13 TSG TUC U2A UG4 UNUBA UOJIU UTJUX UZXMN VC2 VFIZW W23 W48 W92 WK8 YLTOR ~A9 ~WA ABQSL ACUHS AEFQL AGRTI BSONS H13 PQBZA ZMTXR AAYXX ACSTC ADHKG AGQPQ AHPBZ CITATION PHGZM PHGZT TGP 406 7SC 7TB 7XB 8AL 8FD 8FK AACDK AAJBT AAPKM AASML AATNV AAYZH ABAKF ABDBE ABFSG ABRTQ ACAOD ACDTI ACPIV ACZOJ AEMSY AESKC AEZWR AFBBN AFDZB AFHIU AFOHR AGQEE AHWEU AIGIU AIXLP ATHPR DDRTE DPUIP FR3 JQ2 JZLTJ KR7 L.- L.0 L7M L~C L~D NPVJJ PKEHL PQEST PQGLB PQUKI PRINS Q9U SJYHP PUEGO |
| ID | FETCH-LOGICAL-c458t-33fb535bcdfe04b099a65715570d2ac4b5a680a8f151cbb3facb7e9a1d237923 |
| IEDL.DBID | 8FG |
| ISSN | 1673-3452 2731-8648 |
| IngestDate | Fri Sep 05 13:01:47 EDT 2025 Wed Sep 17 23:56:40 EDT 2025 Thu Apr 24 23:05:57 EDT 2025 Tue Jul 01 02:25:47 EDT 2025 Fri Feb 21 02:25:50 EST 2025 Tue Feb 27 04:43:01 EST 2024 Wed Feb 14 10:33:12 EST 2024 |
| IsDoiOpenAccess | true |
| IsOpenAccess | true |
| IsPeerReviewed | true |
| IsScholarly | true |
| Issue | 4 |
| Keywords | recurrence uniqueness moments of return time 60J60 Poisson equation Single birth process ergodicity |
| Language | English |
| License | This is an open-access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. |
| LinkModel | DirectLink |
| MergedId | FETCHMERGED-LOGICAL-c458t-33fb535bcdfe04b099a65715570d2ac4b5a680a8f151cbb3facb7e9a1d237923 |
| Notes | Based on a new explicit representation of the solution to the Poisson equation with respect to single birth processes, the unified treatment for various criteria on classical problems （including uniqueness, recurrence, ergodicity, exponential ergodicity, strong ergodicity, as well as extinction probability, etc.） for the processes are presented. 11-5739/O1 Single birth process, Poisson equation, uniqueness, recurrence,ergodicity, moments of return time recurrence Document accepted on :2014-04-02 uniqueness moments of return time Document received on :2014-03-05 Poisson equation Single birth process ergodicity SourceType-Scholarly Journals-1 ObjectType-Feature-1 content type line 14 ObjectType-Article-2 content type line 23 |
| OpenAccessLink | https://journal.hep.com.cn/fmc/EN/10.1007/s11464-014-0381-7 |
| PQID | 1550483214 |
| PQPubID | 54395 |
| PageCount | 36 |
| ParticipantIDs | proquest_miscellaneous_1567106746 proquest_journals_1550483214 crossref_citationtrail_10_1007_s11464_014_0381_7 crossref_primary_10_1007_s11464_014_0381_7 springer_journals_10_1007_s11464_014_0381_7 higheredpress_frontiers_10_1007_s11464_014_0381_7 chongqing_primary_662063359 |
| ProviderPackageCode | CITATION AAYXX |
| PublicationCentury | 2000 |
| PublicationDate | 2014-08-01 |
| PublicationDateYYYYMMDD | 2014-08-01 |
| PublicationDate_xml | – month: 08 year: 2014 text: 2014-08-01 day: 01 |
| PublicationDecade | 2010 |
| PublicationPlace | Heidelberg |
| PublicationPlace_xml | – name: Heidelberg – name: Dordrecht |
| PublicationSubtitle | Selected Publications from Chinese Universities |
| PublicationTitle | Frontiers of Mathematics |
| PublicationTitleAbbrev | Front. Math. China |
| PublicationTitleAlternate | Frontiers of Mathematics in China |
| PublicationYear | 2014 |
| Publisher | Higher Education Press Springer Nature B.V |
| Publisher_xml | – name: Higher Education Press – name: Springer Nature B.V |
| References | AndersonWJContinuous-Time Markov Chains: An Applications-Oriented Approach1991New YorkSpringer-Verlag10.1007/978-1-4612-3038-00731.60067 ChenM FFrom Markov Chains to Non-Equilibrium Particle Systems20042nd edSingaporeWorld Scientific10.1142/97898125624561078.60003 ZhangY HExpressions on moments of hitting time for single birth process in infinite and finite spaceJ Beijing Normal Univ201349544545206311250 ZhangY HBirth-death-catastrophe type single birth Q-matricesJ Beijing Normal Univ20114743473501265.60164 ChenM FSpeed of stability for birth-death processFront Math China20105337951610.1007/s11464-010-0068-71220.600442660525 ZhangY HStrong ergodicity for single-birth processesJ Appl Probab200138127027710.1239/jap/9969866620984.600831816773 YanS JChenM FMultidimensional Q-processesChin Ann Math Ser B19867901100596.60074851278 BrockwellP JThe extinction time of a general birth and death processes with catastrophesJ Appl Probab19862385185810.2307/32144590614.60081867182 ChenM FExplicit criteria for several types of ergodicityChinese J Appl Probab Statist2001172181874035 WangL DZhangY HCriteria for zero-exit (-entrance) of single-birth (-death) Q-matricesActa Math Sinica (Chin Ser)2014 ZhangY HMoments of the first hitting time for single birth processesJ Beijing Normal Univ20033944304341073.60073 MaoY HErgodic degrees for continuous-time Markov chainsSci China Ser A200447216117410.1360/02ys03061067.600692068936 BrockwellP JGaniJResnickS IBirth, immigration and catastrophe processesAdv in Appl Probab19821470973110.2307/14270200496.92007677553 MaoY HEigentime identity for transient Markov chainsJ Math Anal Appl2006315241542410.1016/j.jmaa.2005.04.0681087.600592202590 ReuterG E HCompetition processesProceedings of the Fourth Berkeley Symposium on Mathematical Statistics and Probability, Vol 21961421430 MaoY HZhangY HExponential ergodicity for single-birth processesJ Appl Probab2004411022103210.1239/jap/11018405481062.600892122477 ZhangJ KOn the generalized birth and death processes (I)Acta Math Sci Ser B Engl Ed19844241259 ZhangY HThe hitting time and stationary distribution for single birth processesJ Beijing Normal Univ20044021571611075.60572 ChenM FSingle birth processesChin Ann Math Ser B199920778210.1142/S02529599990001140922.60068 ChenM FZhangXIsospectral operators2014 HouZ TGuoQ FHomogeneous Denumerable Markov Processes1978BeijingScience Press G E H Reuter (381_CR13) 1961 Z T Hou (381_CR9) 1978 Y H Zhang (381_CR19) 2004; 40 M F Chen (381_CR7) 2010; 5 WJ Anderson (381_CR1) 1991 P J Brockwell (381_CR3) 1982; 14 Y H Zhang (381_CR18) 2003; 39 L D Wang (381_CR14) 2014 M F Chen (381_CR8) 2014 P J Brockwell (381_CR2) 1986; 23 M F Chen (381_CR5) 2001; 17 M F Chen (381_CR4) 1999; 20 M F Chen (381_CR6) 2004 Y H Mao (381_CR10) 2004; 47 J K Zhang (381_CR16) 1984; 4 S J Yan (381_CR15) 1986; 7 Y H Mao (381_CR12) 2004; 41 Y H Zhang (381_CR17) 2001; 38 Y H Zhang (381_CR21) 2013; 49 Y H Zhang (381_CR20) 2011; 47 Y H Mao (381_CR11) 2006; 315 |
| References_xml | – reference: ZhangY HStrong ergodicity for single-birth processesJ Appl Probab200138127027710.1239/jap/9969866620984.600831816773 – reference: BrockwellP JGaniJResnickS IBirth, immigration and catastrophe processesAdv in Appl Probab19821470973110.2307/14270200496.92007677553 – reference: ZhangY HBirth-death-catastrophe type single birth Q-matricesJ Beijing Normal Univ20114743473501265.60164 – reference: ChenM FSpeed of stability for birth-death processFront Math China20105337951610.1007/s11464-010-0068-71220.600442660525 – reference: ChenM FZhangXIsospectral operators2014 – reference: MaoY HEigentime identity for transient Markov chainsJ Math Anal Appl2006315241542410.1016/j.jmaa.2005.04.0681087.600592202590 – reference: MaoY HZhangY HExponential ergodicity for single-birth processesJ Appl Probab2004411022103210.1239/jap/11018405481062.600892122477 – reference: ReuterG E HCompetition processesProceedings of the Fourth Berkeley Symposium on Mathematical Statistics and Probability, Vol 21961421430 – reference: AndersonWJContinuous-Time Markov Chains: An Applications-Oriented Approach1991New YorkSpringer-Verlag10.1007/978-1-4612-3038-00731.60067 – reference: BrockwellP JThe extinction time of a general birth and death processes with catastrophesJ Appl Probab19862385185810.2307/32144590614.60081867182 – reference: HouZ TGuoQ FHomogeneous Denumerable Markov Processes1978BeijingScience Press – reference: YanS JChenM FMultidimensional Q-processesChin Ann Math Ser B19867901100596.60074851278 – reference: ZhangY HThe hitting time and stationary distribution for single birth processesJ Beijing Normal Univ20044021571611075.60572 – reference: WangL DZhangY HCriteria for zero-exit (-entrance) of single-birth (-death) Q-matricesActa Math Sinica (Chin Ser)2014 – reference: ChenM FSingle birth processesChin Ann Math Ser B199920778210.1142/S02529599990001140922.60068 – reference: ZhangY HMoments of the first hitting time for single birth processesJ Beijing Normal Univ20033944304341073.60073 – reference: ChenM FFrom Markov Chains to Non-Equilibrium Particle Systems20042nd edSingaporeWorld Scientific10.1142/97898125624561078.60003 – reference: ZhangJ KOn the generalized birth and death processes (I)Acta Math Sci Ser B Engl Ed19844241259 – reference: ChenM FExplicit criteria for several types of ergodicityChinese J Appl Probab Statist2001172181874035 – reference: ZhangY HExpressions on moments of hitting time for single birth process in infinite and finite spaceJ Beijing Normal Univ201349544545206311250 – reference: MaoY HErgodic degrees for continuous-time Markov chainsSci China Ser A200447216117410.1360/02ys03061067.600692068936 – volume: 17 start-page: 1 issue: 2 year: 2001 ident: 381_CR5 publication-title: Chinese J Appl Probab Statist – volume: 5 start-page: 379 issue: 3 year: 2010 ident: 381_CR7 publication-title: Front Math China doi: 10.1007/s11464-010-0068-7 – volume: 38 start-page: 270 issue: 1 year: 2001 ident: 381_CR17 publication-title: J Appl Probab doi: 10.1239/jap/996986662 – volume: 39 start-page: 430 issue: 4 year: 2003 ident: 381_CR18 publication-title: J Beijing Normal Univ – volume-title: Isospectral operators year: 2014 ident: 381_CR8 – volume-title: Homogeneous Denumerable Markov Processes year: 1978 ident: 381_CR9 – volume: 20 start-page: 77 year: 1999 ident: 381_CR4 publication-title: Chin Ann Math Ser B doi: 10.1142/S0252959999000114 – volume-title: Acta Math Sinica (Chin Ser) year: 2014 ident: 381_CR14 – volume: 41 start-page: 1022 year: 2004 ident: 381_CR12 publication-title: J Appl Probab doi: 10.1239/jap/1101840548 – volume: 47 start-page: 347 issue: 4 year: 2011 ident: 381_CR20 publication-title: J Beijing Normal Univ – volume: 4 start-page: 241 year: 1984 ident: 381_CR16 publication-title: Acta Math Sci Ser B Engl Ed – volume-title: From Markov Chains to Non-Equilibrium Particle Systems year: 2004 ident: 381_CR6 doi: 10.1142/5513 – volume: 14 start-page: 709 year: 1982 ident: 381_CR3 publication-title: Adv in Appl Probab doi: 10.2307/1427020 – volume: 7 start-page: 90 year: 1986 ident: 381_CR15 publication-title: Chin Ann Math Ser B – volume: 49 start-page: 445 issue: 5 year: 2013 ident: 381_CR21 publication-title: J Beijing Normal Univ – volume-title: Continuous-Time Markov Chains: An Applications-Oriented Approach year: 1991 ident: 381_CR1 doi: 10.1007/978-1-4612-3038-0 – volume: 47 start-page: 161 issue: 2 year: 2004 ident: 381_CR10 publication-title: Sci China Ser A doi: 10.1360/02ys0306 – volume: 23 start-page: 851 year: 1986 ident: 381_CR2 publication-title: J Appl Probab doi: 10.2307/3214459 – volume: 315 start-page: 415 issue: 2 year: 2006 ident: 381_CR11 publication-title: J Math Anal Appl doi: 10.1016/j.jmaa.2005.04.068 – start-page: 421 volume-title: Proceedings of the Fourth Berkeley Symposium on Mathematical Statistics and Probability, Vol 2 year: 1961 ident: 381_CR13 – volume: 40 start-page: 157 issue: 2 year: 2004 ident: 381_CR19 publication-title: J Beijing Normal Univ |
| SSID | ssj0051659 ssj0002902061 |
| Score | 2.0969799 |
| Snippet | Based on a new explicit representation of the solution to the Poisson equation with respect to single birth processes, the unified treatment for various... Issue Title: Markov Processes and Related Topics Based on a new explicit representation of the solution to the Poisson equation with respect to single birth... |
| SourceID | proquest crossref springer higheredpress chongqing |
| SourceType | Aggregation Database Enrichment Source Index Database Publisher |
| StartPage | 761 |
| SubjectTerms | Birth China Criteria Ergodic processes ergodicity Laplace transforms Linear equations Mathematical analysis Mathematics Mathematics and Statistics moments of return time Poisson distribution Poisson equation recurrence Representations Research Article Single birth process Studies Uniqueness 公式 单生过程 强遍历性 泊松方程 灭绝概率 统一处理 |
| SummonAdditionalLinks | – databaseName: SpringerLink Journals (ICM) dbid: U2A link: http://utb.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwlV1LS8QwEA66XhQRn1hdpYInpdDm1e5xEWUR9KTgLSRp6gpLd93H_3cm21RXVPBQKM00gZk8vnZmviHk0khDs5KJhBbCJZxamegcSwJqXZnM5innmCj88CgHz_z-Rbw0edyzEO0eXJJ-p_5MdoNFjRETcMExk-TrZEMgnRRM4mfaD9uvyKSvkJbJnCWMCxpcmT91gYQKw3H9-g7DrRxM20MfZeFKH426gj6_OUz9OXS3S3YaABn3lxbfI2uu3idbDy376uyAIPNrBdAy9oyVIbuojsdVjBB1AYAZb2L8TTBysXmbzofxZJkx4GaH5Onu9ulmkDRlEhLLRTFPGKuMYMLYsnIpNwD5tBR5htxaJdWWG6FlkeqigsPdGsMqbU3uejorKUP2wCPSqce1OyYxZdJJanuSasqZYSYVQmt4VNrCWd2LyGmrLjVZsmEoKSnAHCagNQ0KVLYhGMc6FyP1SY2M-legf4X6V3lErtpXQn9_CGcrVlEVUjxgwfC_3ukGy6lmcYI0fJVxX6EpIhdtMywr9JXo2o0XKCNzZNfjMiLXweJfuvhtwJN_SZ-STepnIwYUdklnPl24MwA5c3PuJ_UHD_Dw6g priority: 102 providerName: Springer Nature |
| Title | Unified representation of formulas for single birth processes |
| URI | http://lib.cqvip.com/qk/71243X/201404/662063359.html https://journal.hep.com.cn/fmc/EN/10.1007/s11464-014-0381-7 https://link.springer.com/article/10.1007/s11464-014-0381-7 https://www.proquest.com/docview/1550483214 https://www.proquest.com/docview/1567106746 |
| Volume | 9 |
| hasFullText | 1 |
| inHoldings | 1 |
| isFullTextHit | |
| isPrint | |
| link | http://utb.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwfV3da9swEBdd81IYo6UrzdoGD_a0IWrry87TSErSsrFQSgLtk5BkuSkUO22T_393iu02hebByFiyBKeP-3G6-x0hP6yyLMm5pCyTngrmFDUppgQ0prCJS2MhMFD430RdzcSfW3lbG9xearfK5kwMB3VeObSRnyOUFiGtzu_FE8WsUXi7WqfQ-EQ6CQNdi5Hi48vWxsL6AIYCZSoo6YRmSmTNxWaInoNTAl0w4AG9RVOkV5hX5f0TKI0NNfV5HnwufB58Uzew6Lvr06CVxvvkSw0no8F6_g_Iji8PCTK_FgAto8BY2UQXlVFVRAhRVwCY8SVCM8Gjj-zD83IeLdYRA_7lK5mOR9OLK1qnSaBOyGxJOS-s5NK6vPCxsAD5jJJpgtxaOTNOWGlUFpusAOXurOWFcTb1fZPkjCN74BHZLavSH5OIceUVc33FDBPcchtLaQx8yl3mnel3yUkrIL1Ys2FopUDGnEuojRuRaVcTjGOei0f9So2MEtcgcY0S12mX_Gx_afrb0jjZmAddIMUDJgzf9s9pM1e63pzQul1KXfK9rYZthXclpvTVCtuoFNn1hOqSX80cv-niowG_bR_whOyxsODQg_CU7C6fV_4MUM3S9sLS7ZHOYDwcTrC8vPs7gnI4mlzfQO2MDf4DF-T16Q |
| linkProvider | ProQuest |
| linkToHtml | http://utb.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwtV3daxQxEB9qfVAQUVQ8W20EfVGCu_navQcpRT2v9uPphL6FJJvtCWX32t4h_lH-j87kblev4L31YWHZfMFkkvltMvMbgDfeeJFXUnNR6siVCIa7glICOlf7PBSZUhQofHJqxt_VtzN9tgW_u1gYcqvs9sS0UVdtoDPyDwSlVUqrsz-75JQ1im5XuxQaS7U4ir9-4i_b9cfDzzi_b4UYfZl8GvNVVgEelC7nXMraa6l9qOqYKY8IyRld5ERFVQkXlNfOlJkra7SFwXtZu-CLOHR5JSSR7WG3d-CuklKSB2E5-tof6YghYq_E0IqYIOelUWV3j5qC9XBTIo8PfNBM8oLYHKZtc36JNmrNKj6YJhePWCVX2DXoe-O2NhnB0SN4uEKv7GCpbo9hKzZPgIhma0SyLBFkdsFMDWtrRoh4gficXhidSlxE5n9czadstgxQiNdPYXIb8nsG203bxOfAhDTRiDA0wgklvfSZ1s7hpyqUMbjhAHZ6AdnZknzDGoMyRtljadaJzIYVnzml1biwf5mYSeIWJW5J4rYYwLu-Sdffhsr52jzYmhglKD_5pja73VzZ1V6AtXvNHcDrvhhXMV3NuCa2C6pjCiLzU2YA77s5_qeL_w34YvOAe3BvPDk5tseHp0c7cF8k5SPnxV3Ynl8t4ksEVHP_KqkxA3vLy-YPtcstRQ |
| linkToPdf | http://utb.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwlV3dS9xAEB-sQmkRsbal56mN4FNLMNmv5B4P9bAfig8Kvi27m91eQXJXL_f_O5PLnl5pBR8CIfsFM7uZXzIzvwE4ssqyvOIyZaX0qWBOpaagkoDGBJu7IhOCEoUvLtX5jfh-K2-7OqezGO0eXZKLnAZiaaqb42kVjh8T3_CAU_QEXmhy0uIVbAg01RTTdcOG8VUsc9VWS8tVwVMuJItuzX9NQeQK40n96w8uvWKkNsdtxIWv2sjUFST6l_O0tUmjbdjqwGQyXGj_Haz5egfeXiyZWGfvgVhgA8LMpGWvjJlGdTIJCcHVOYJnuknol8GdT-zv-2acTBfZA372Aa5HZ9cn52lXMiF1QpZNynmwkkvrquAzYRH-GSWLnHi2KmacsNKoMjNlQEPvrOXBOFv4gckrxolJ8COs15Paf4KEceUVcwPFDBPccptJaQw-qlzpnRn0oL8Ul54umDG0UgwhD5fYmkUBateRjVPNizv9SJNM8tcof03y10UPviyHxPme6ZyvaEUHonug4uHPjdmLmtPdQcXe-IUm2mpNPThcNuMRI7-Jqf1kTn1UQUx7QvXga9T4kyn-t-Dui3p_htdXpyP989vljz68Ye3GpDjDPVhv7ud-H7FPYw_a_f0AoML4Eg |
| 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=Unified+representation+of+formulas+for+single+birth+processes&rft.jtitle=Frontiers+of+mathematics+in+China&rft.au=CHEN%2C+Mu-Fa&rft.au=ZHANG%2C+Yuhui&rft.date=2014-08-01&rft.pub=Higher+Education+Press&rft.issn=1673-3452&rft.eissn=1673-3576&rft.volume=9&rft.issue=4&rft.spage=761&rft.epage=796&rft_id=info:doi/10.1007%2Fs11464-014-0381-7&rft.externalDBID=n%2Fa&rft.externalDocID=10.1007%2Fs11464-014-0381-7 |
| thumbnail_s | http://utb.summon.serialssolutions.com/2.0.0/image/custom?url=http%3A%2F%2Fimage.cqvip.com%2Fvip1000%2Fqk%2F71243X%2F71243X.jpg |