Mean field games with common noise | Zendy

René Carmona | Zendy; François Delarue | Zendy; Daniel Lacker | Zendy

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Mean field games with common noise

Author(s) -

René Carmona,

François Delarue,

Daniel Lacker

Publication year - 2016

Publication title -

the annals of probability

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 3.184

H-Index - 98

eISSN - 2168-894X

pISSN - 0091-1798

DOI - 10.1214/15-aop1060

Subject(s) - noise (video) , field (mathematics) , computer science , acoustics , mathematics , physics , artificial intelligence , pure mathematics , image (mathematics)

A theory of existence and uniqueness is developed for general stochastic differential mean field games with common noise. The concepts of strong and weak solutions are introduced in analogy with the theory of stochastic differential equations, and existence of weak solutions for mean field games is shown to hold under very general assumptions. Examples and counter-examples are provided to enlighten the underpinnings of the existence theory. Finally, an analog of the famous result of Yamada and Watanabe is derived, and it is used to prove existence and uniqueness of a strong solution under additional assumptions.

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