On the $l_p$ stability estimates for stochastic and deterministic difference equations and their application to SPDEs and PDEs
Probability
2019-10-31 v1 Numerical Analysis
Analysis of PDEs
Numerical Analysis
Abstract
In this paper we develop the -theory of space-time stochastic difference equations which can be considered as a discrete counterpart of N.V. Krylov's -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.
Keywords
Cite
@article{arxiv.1910.13640,
title = {On the $l_p$ stability estimates for stochastic and deterministic difference equations and their application to SPDEs and PDEs},
author = {Timur Yastrzhembskiy},
journal= {arXiv preprint arXiv:1910.13640},
year = {2019}
}