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...

Full description

Saved in:
Bibliographic Details
Published inJournal of evolution equations Vol. 21; no. 2; pp. 2009 - 2045
Main Author Wang, Feng-Yu
Format Journal Article
LanguageEnglish
Published Cham Springer International Publishing 01.06.2021
Springer Nature B.V
Subjects
Analysis
Mathematics
Mathematics and Statistics
58J65
60J60
Intrinsic/Lions derivative
Ergodicity
Measure-valued diffusion process
Image dependent SDE
Feynman–Kac formula
Online AccessGet full text
ISSN1424-3199
1424-3202
DOI10.1007/s00028-020-00665-z

Cover

More Information
Summary: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.
Bibliography:ObjectType-Article-1
SourceType-Scholarly Journals-1
ObjectType-Feature-2
content type line 14
ISSN:1424-3199
1424-3202
DOI:10.1007/s00028-020-00665-z