Image-dependent conditional McKean–Vlasov SDEs for measure-valued diffusion processes
We consider a special class of mean field SDEs with common noise which depends on the image of the solution (i.e., the conditional distribution given noise). The strong well-posedness is derived under a monotone condition which is weaker than those used in the literature of mean field games; the Fey...
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| Published in | Journal of evolution equations Vol. 21; no. 2; pp. 2009 - 2045 |
|---|---|
| Main Author | |
| Format | Journal Article |
| Language | English |
| Published |
Cham
Springer International Publishing
01.06.2021
Springer Nature B.V |
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| ISSN | 1424-3199 1424-3202 |
| DOI | 10.1007/s00028-020-00665-z |
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| Abstract | We consider a special class of mean field SDEs with common noise which depends on the image of the solution (i.e., the conditional distribution given noise). The strong well-posedness is derived under a monotone condition which is weaker than those used in the literature of mean field games; the Feynman–Kac formula is established to solve Schrördinegr type PDEs on
P
2
, and the ergodicity is proved for a class of measure-valued diffusion processes. |
|---|---|
| AbstractList | We consider a special class of mean field SDEs with common noise which depends on the image of the solution (i.e., the conditional distribution given noise). The strong well-posedness is derived under a monotone condition which is weaker than those used in the literature of mean field games; the Feynman–Kac formula is established to solve Schrördinegr type PDEs on P2, and the ergodicity is proved for a class of measure-valued diffusion processes. We consider a special class of mean field SDEs with common noise which depends on the image of the solution (i.e., the conditional distribution given noise). The strong well-posedness is derived under a monotone condition which is weaker than those used in the literature of mean field games; the Feynman–Kac formula is established to solve Schrördinegr type PDEs on P 2 , and the ergodicity is proved for a class of measure-valued diffusion processes. |
| Author | Wang, Feng-Yu |
| Author_xml | – sequence: 1 givenname: Feng-Yu surname: Wang fullname: Wang, Feng-Yu email: wangfy@tju.edu.cn, F.-Y.Wang@swansea.ac.uk organization: Center for Applied Mathematics, Tianjin University, Department of Mathematics, Swansea University |
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| Cites_doi | 10.1016/j.jmaa.2019.123624 10.1016/j.jfa.2015.06.007 10.1214/16-AOP1137 10.1016/j.spa.2017.05.006 10.1007/s11464-019-0807-3 10.1007/s11537-007-0657-8 10.23943/princeton/9780691190716.001.0001 10.1002/cpa.21758 10.1007/978-3-319-56436-4 10.1109/TAC.2007.904450 10.1016/j.crma.2006.09.019 10.1016/S1874-5717(07)80004-1 |
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| Keywords | 58J65 60J60 Intrinsic/Lions derivative Ergodicity Measure-valued diffusion process Image dependent SDE Feynman–Kac formula |
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| Title | Image-dependent conditional McKean–Vlasov SDEs for measure-valued diffusion processes |
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