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Noise through an additional variable for mean field games master equation on finite state space

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arxiv 2402.05635 v2 pith:TGNXOB6Q submitted 2024-02-08 math.AP

Charles Bertucci (CMAP) , Charles Meynard (CMAP) This is my paper · ORCID
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keywords equationmasterstateadditionalfinitemodellingnoiseprocess
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This paper provides a mathematical study of the well-posedness of master equation on finite state space involving terms modelling common noise. In this setting, the solution of the master equation depends on an additional variable modelling the value of a stochastic process impacting all players. Using technique from viscosity solutions, we give sufficient conditions for the existence of a Lipschitz continuous solution on any time interval. Under some structural assumptions, we are even able to treat cases in which the dynamics of this stochastic process depend on the state of the game.

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Cited by 2 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. A study of common noise in mean field games

    math.AP 2024-12 conditional novelty 6.0 of 10

    The paper proves global well-posedness of mean field games master equations with an endogenous common noise variable under flat or L2/displacement monotonicity conditions, including in the presence of additive common noise.

  2. Analysis on spaces of measures

    math.AP 2026-07 conditional novelty 4.0 of 10

    A synthesis monograph unifying vertical and horizontal differential calculus on spaces of measures, applied to well-posedness of monotone mean field game master equations and to viscosity solutions of mean field Hamil...

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