On moments and strong local Hölder regularity of solutions of stochastic differential equations and of their spatial derivative processes

2019/03/22 by Anselm Hudde, Hudde, Anselm, Martin Hutzenthaler +3
Economics, Econometrics and Finance · Mathematics · Social Sciences · #FOS: Mathematics #Insurance, Mortality, Demography, Risk Management #Mathematical Biology Tumor Growth #Probability (math.PR) #Stochastic processes and financial applications

paper · pdf · doi:10.48550/arxiv.1903.09707

openalex publication_date 2019/03/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Spatial differentiability of solutions of stochastic differential equations (SDEs) is a classical question in stochastic analysis. The case of coefficients with globally Lipschitz continuous derivatives is well understood in the literature. Counterexamples with smooth and bounded coefficients demonstrate that the non-globally Lipschitz case is more subtle. In this article we establish conditions, including a suitable local monotonicity property, which provide existence of continuously differentiable solutions of SDEs, moment estimates and strong local Hölder regularity.

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