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A Cauchy-Kovalevskaya theorem for the mean field games system
Dissertation   Open access

A Cauchy-Kovalevskaya theorem for the mean field games system

Benjamin T. Irwin
Doctor of Philosophy (Ph.D.), Drexel University
Jun 2021
DOI:
https://doi.org/10.17918/00000793
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Abstract

Mean field theory
The mean field games system of partial differential equations is comprised of a backward parabolic Hamilton-Jacobi-Bellman equation and a forward parabolic Fokker-Planck equation. We prove an abstract Cauchy-Kovalevskaya theorem for forward-backward systems, which we then apply to prove existence of solutions to the mean field games system. We then show that the zero diffusion limit may be taken, proving that solutions of the first-order mean field games system are the zero diffusion limit of the solutions of the parabolic mean field games system.

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