Malliavin Calculus for rough stochastic differential equations

2024/02/19 by Fabio Bugini, Bugini, Fabio, Michele Coghi +3 · 4 citations
Economics, Econometrics and Finance · #60H07 #60H10 #60L20 #FOS: Mathematics #Probability (math.PR) #Stochastic processes and financial applications

paper · pdf · doi:10.48550/arxiv.2402.12056

openalex publication_date 2024/02/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this work we show that rough stochastic differential equations (RSDEs), as introduced by Friz, Hocquet, and Lê (2021), are Malliavin differentiable. We use this to prove existence of a density when the diffusion coefficients satisfies standard ellipticity assumptions. Moreover, when the coefficients are smooth and the diffusion coefficients satisfies a Hörmander condition, the density is shown to be smooth. The key ingredient is to develop a comprehensive theory of linear rough stochastic differential equations, which could be of independent interest.

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