Compensated stochastic theta methods for stochastic differential equations with jumps
type: Item
instance of: scholarly article
title: Compensated stochastic theta methods for stochastic differential equations with jumps
zbMATH Open document ID: 1198.65034
published in: Applied Numerical Mathematics
publication date: 2010-08-13T00:00:00Z
review text: Compensated stochastic theta methods (CSTM) for approximating the solutions of jumpdiffusion Ito stochastic differential equations of the form \[ dX(t)= f(X(t-))\,dt+ g(X(t-))\,dW(t)+ h(X(t-))\,dN(t),\;t> 0,\;X(0-)= X_0 \] are introduced. Mean-square convergence, A-stability, and exponential stability of CSTM methods are proved. Results of numerical experiments are presented that demonstrate a stability advantage of CSTM over stochastic theta methods.
reviewed by: Melvin D. Lax
Mathematics Subject Classification ID: 65C30
zbMATH DE Number: 5770451
zbMATH Keywords: stochastic theta methods
zbMATH Keywords: jump-diffusion
zbMATH Keywords: compensated Poisson process
zbMATH Keywords: strong convergence
zbMATH Keywords: A-stability
zbMATH Keywords: B-stability
zbMATH Keywords: exponential mean-square stability
author: Xiaojie Wang
author: Siqing Gan
describes a project that uses: RODAS
MaRDI profile type: Publication
full work available at URL: j.apnum.2010.04.012
OpenAlex ID: W2089539503
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DOI: 10.1016/J.APNUM.2010.04.012
description: scientific article; zbMATH DE number 5770451