The Donsker delta function and local time for McKean-Vlasov processes and applications
Probability
2023-02-27 v1 Functional Analysis
Optimization and Control
Abstract
The purpose of this paper is to establish a stochastic differential equation for the Donsker delta measure of the solution of a McKean-Vlasov (mean-field) stochastic differential equation. If the Donsker delta measure is absolutely continuous with respect to Lebesgue measure, then its Radon-Nikodym derivative is called the Donsker delta function. In that case it can be proved that the local time of such a process is simply the integral with respect to time of the Donsker delta function. Therefore we also get an equation for the local time of such a process. For some particular McKean-Vlasov processes, we find explicit expressions for their Donsker delta functions and hence for their local times.
Cite
@article{arxiv.2302.12522,
title = {The Donsker delta function and local time for McKean-Vlasov processes and applications},
author = {Nacira Agram and Bernt Øksendal},
journal= {arXiv preprint arXiv:2302.12522},
year = {2023}
}