Mean field stochastic differential equations with a diffusion coefficient with irregular distributional dependence

2025/03/27 by Jani Nykänen, Nykänen, Jani
Computer Science · Economics, Econometrics and Finance · Mathematics · #60H10 #60H30 #Advanced Mathematical Modeling in Engineering #Differential Equations and Numerical Methods #FOS: Mathematics #Probability (math.PR) #Stochastic processes and financial applications

paper · pdf · doi:10.48550/arxiv.2503.21475

openalex publication_date 2025/03/27 · openalex created_date 2025/10/11 · openalex updated_date 2026/08/02

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.

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