• Corpus ID: 214743428

Superposition and mimicking theorems for conditional McKean-Vlasov equations

@article{Lacker2020SuperpositionAM,
  title={Superposition and mimicking theorems for conditional McKean-Vlasov equations},
  author={Daniel Lacker and Mykhaylo Shkolnikov and Jiacheng Zhang},
  journal={arXiv: Probability},
  year={2020}
}
We consider conditional McKean-Vlasov stochastic differential equations (SDEs), such as the ones arising in the large-system limit of mean field games and particle systems with mean field interactions when common noise is present. The conditional time-marginals of the solutions to these SDEs satisfy non-linear stochastic partial differential equations (SPDEs) of the second order, whereas the laws of the conditional time-marginals follow Fokker-Planck equations on the space of probability… 
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