Mean field stochastic differential equations with a diffusion coefficient with irregular distributional dependence
Probability
2025-03-28 v1
Abstract
We study mean field stochastic differential equations with a diffusion coefficient that depends on the distribution function of the unknown process in a discontinuous manner, which is a type of distribution dependent regime switching. To determine the distribution function we show that under certain conditions these equations can be transformed into SDEs with deterministic coefficients using a Lamperti-type transformation. We prove an existence and uniqueness result and consider cases when the uniqueness may fail or a solution exists only for a finite time.
Cite
@article{arxiv.2503.21475,
title = {Mean field stochastic differential equations with a diffusion coefficient with irregular distributional dependence},
author = {Jani Nykänen},
journal= {arXiv preprint arXiv:2503.21475},
year = {2025}
}