English

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 lpl_p-theory of space-time stochastic difference equations which can be considered as a discrete counterpart of N.V. Krylov's LpL_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.

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}
}