Regularity of stochastic differential equations on the Wiener space by coupling

Stefan Geiss; Xilin Zhou

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arXiv · 2412.10836

Regularity of stochastic differential equations on the Wiener space by coupling

Stefan Geiss·Xilin Zhou

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Abstract

Using the coupling method introduced in \cite{Geiss:Ylinen:21}, we investigate regularity properties of stochastic differential equations, where we consider the Lipschitz case in $\R^d$ and allow for H\"older continuity of the diffusion coefficient of scalar valued stochastic differential equations. Two cases of the coupling method are of special interest: The uniform coupling to treat the Malliavin Sobolev space $\D_{1,2}$ and real interpolation spaces, and secondly a cut-off coupling to treat the $L_p$-variation of backward stochastic differential equations where the forward process is the investigated stochastic differential equation.

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Stefan Geiss, Xilin Zhou. 2024-12-14. Regularity of stochastic differential equations on the Wiener space by coupling. https://arxiv.org/abs/2412.10836

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