2023/10/20 by Gonçalo dos Reis, Reis, Goncalo dos, Zachary James Wilde +1 · 1 citation
Economics, Econometrics and Finance · Physics and Astronomy · #Advanced Thermodynamics and Statistical Mechanics #FOS: Mathematics #Probability (math.PR) #Stochastic processes and financial applications
paper · doi:10.48550/arxiv.2310.13400
openalex publication_date 2023/10/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this short note, we establish Malliavin differentiability of McKean-Vlasov Stochastic Differential Equations (MV-SDEs) with drifts satisfying both a locally Lipschitz and a one-sided Lipschitz assumption, and where the diffusion coefficient is assumed to be uniformly Lipschitz in its variables. As a secondary contribution, we investigate how Malliavin differentiability transfers across the interacting particle system associated with the McKean-Vlasov equation to its limiting equation. This final result requires both spatial and measure differentiability of the coefficients and doubles as a standalone result of independent interest since the study of Malliavin derivatives of weakly interacting particle systems seems novel to the literature. The presentation is didactic and finishes with a discussion on mollification techniques for the Lions derivative.