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arXiv · 1903.09707

On moments and strong local H\"older regularity of solutions of stochastic differential equations and of their spatial derivative processes

Anselm Hudde·Martin Hutzenthaler·Sara Mazzonetto
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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 H\"older regularity.

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Anselm Hudde, Martin Hutzenthaler, Sara Mazzonetto. 2019-03-22. On moments and strong local H\"older regularity of solutions of stochastic differential equations and of their spatial derivative processes. https://arxiv.org/abs/1903.09707

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