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Mean square convergence of a semidiscrete scheme for SPDEs of Zakai type driven by square integrable martingales

Conference paper
Authors Annika Lang
Published in Procedia Computer Science
Volume 1
Issue 1
Pages 1615-1623
ISSN 1877-0509
Publication year 2010
Published at Department of Mathematical Sciences, Mathematical Statistics
Pages 1615-1623
Language en
Links dx.doi.org/10.1016/j.procs.2010.04....
Keywords Euler-Maruyama scheme , Lévy process , Mean square convergence , Numerical scheme , Stochastic partial differential equations , Zakai equation
Subject categories Probability Theory and Statistics, Numerical analysis

Abstract

In this short note, a direct proof of L2 convergence of an Euler-Maruyama approximation of a Zakai equation driven by a square integrable martingale is shown. The order of convergence is as known for real-valued stochastic differential equations and for less general driving noises O(√Δt) for a time discretization step size Δt. © 2010 Published by Elsevier Ltd.

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