Mean field games with common noise

2014/07/23 by René Carmona, Rene Carmona, Francois Delarue +5 · 19 citations
Economics, Econometrics and Finance · Mathematics · #Analogy #Applied mathematics #Artificial intelligence #Calculus (dental) #Computer science #Differential (mechanical device) #Epistemology #FOS: Mathematics #Field (mathematics) #Mathematical Dynamics and Fractals #Mathematical analysis #Mathematical economics #Mathematics #Mean field theory #Noise (video) #Ordered field #Physics #Probability (math.PR) #Pure mathematics #Quantum mechanics #Stochastic differential equation #Stochastic processes and financial applications #Stochastic processes and statistical mechanics #Uniqueness #math.PR

paper · pdf · doi:10.48550/arxiv.1407.6181

published in arXiv (Cornell University) (Cornell University)

openalex publication_date 2014/07/23 · arxiv created 2015/05/20 · arxiv updated 2015/05/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/04

Abstract

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.

Citations

• Foundations of Modern Probability
• Mean Field Games and Systemic Risk

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