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Image Dependent Conditional McKean-Vlasov SDEs for Measure-Valued Diffusion Processes

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arxiv 1903.02148 v4 pith:ALMUP7UW submitted 2019-03-06 math.PR

classification math.PR
keywords classconditionaldiffusionfieldimagemeanmeasure-valuednoise
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abstract

We consider a special class of mean field SDEs with common noise which depend 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 Schr\"ordinegr type PDEs on $\scr P_2$, and the ergodicity is proved for a class of measure-valued diffusion processes.

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  1. Derivative Formulas in Measure on Riemannian Manifolds

    math.PR 2019-08 accept novelty 7.0 of 10

    For functions of measures on Riemannian manifolds, the intrinsic and Lions derivatives coincide and equal the gradient of the extrinsic derivative, giving a direct limit formula for computing them.

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