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

10/30/2019

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by   Timur Yastrzhembskiy, et al.

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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.