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Translation invariant mean field games with common noise. (English) Zbl 1332.60102
Summary: This note highlights a special class of mean field games in which the coefficients satisfy a convolution-type structural condition. A mean field game of this type with common noise is related to a certain mean field game without common noise by a simple transformation, which permits a tractable construction of a solution of the problem with common noise from a solution of the problem without. This yields new existence results for common noise problems, notably allowing controlled volatility, as well as new uniqueness results for problems without common noise.

60H30 Applications of stochastic analysis (to PDEs, etc.)
60H10 Stochastic ordinary differential equations (aspects of stochastic analysis)
91A15 Stochastic games, stochastic differential games
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