Mean field stochastic differential equations with a discontinuous diffusion coefficient

2022/06/23 by Jani Nykänen, Nykänen, Jani
Economics, Econometrics and Finance · Mathematics · #FOS: Mathematics #Mathematical Biology Tumor Growth #Probability (math.PR) #Stochastic processes and financial applications #Stochastic processes and statistical mechanics

paper · pdf · doi:10.48550/arxiv.2206.11538

openalex publication_date 2022/06/23 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We study ℝ^d-valued mean field stochastic differential equations with a diffusion coefficient depending on the L_p-norm of the process in a discontinuous way. We show that under a strong drift there exists a unique global strong solution and consider typical cases where the existence of a global solution fails.

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