On the $l_p$ stability estimates for stochastic and deterministic difference equations and their application to SPDEs and PDEs

Timur Yastrzhembskiy

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arXiv · 1910.13640

On the $l_p$ stability estimates for stochastic and deterministic difference equations and their application to SPDEs and PDEs

Timur Yastrzhembskiy

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Abstract

In this paper we develop the $l_p$-theory of space-time stochastic difference equations which can be considered as a discrete counterpart of N.V. Krylov's $L_p$-theory of stochastic partial differential equations. We also prove a Calderon-Zygmund type estimate for deterministic parabolic finite difference schemes with variable coefficients under relaxed assumptions on the coefficients, the initial data and the forcing term.

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BibTeX RIS

Timur Yastrzhembskiy. 2019-10-30. On the $l_p$ stability estimates for stochastic and deterministic difference equations and their application to SPDEs and PDEs. https://arxiv.org/abs/1910.13640

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