Solving mean field rough differential equations

I. Bailleul; R. Catellier; F. Delarue

Solving mean field rough differential equations

Probability 2019-07-02 v2 Classical Analysis and ODEs

Authors: I. Bailleul , R. Catellier , F. Delarue

Abstract

We provide in this work a robust solution theory for random rough differential equations of mean field type $dX_t = V(X_t,\mathcal{L}(X_t))dt + F(X_t,\mathcal{L}(X_t))dW_t,$ where $W$ is a random rough path and $\mathcal{L}(X_t)$ stands for the law of $X_t$ , with mean field interaction in both the drift and diffusivity. The analysis requires the introduction of a new rough path-like setting and an associated notion of controlled path. We use crucially Lions' approach to differential calculus on Wasserstein space along the way.

Cite

@article{arxiv.1802.05882,
  title  = {Solving mean field rough differential equations},
  author = {I. Bailleul and R. Catellier and F. Delarue},
  journal= {arXiv preprint arXiv:1802.05882},
  year   = {2019}
}

Comments

63 pages; v2: Version 1 of this work has been split in two seperate works, the first part of which is the present work. A number of arguments in both parts have been reworked in depth, and improved

Solving mean field rough differential equations

Abstract

Cite

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