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

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