Ito-Wentzell-Lions formula for measure dependent random fields under full and conditional measure flows

Abstract

We present several Ito-Wentzell formulae on Wiener spaces for real-valued functional random field of Ito type that depend on measure flows. We distinguish the full- and the marginal-measure flow cases in the spirit of mean-field games. Derivatives with respect to the measure components are understood in the sense of Lions.

arXiv comment31 pages