Communications in Mathematical Sciences

Volume 10 (2012)

Number 4

Two-stage stochasticRunge-Kutta methods for stochastic differential equations with jump diffusion

Pages: 1317 – 1329

(Fast Communication)

DOI: http://dx.doi.org/10.4310/CMS.2012.v10.n4.a15

Authors

Can Huang (Department of Mathematics, Wayne State University, Detroit, Michigan)

Jing Shi (Department of Mathematics, Wayne State University, Detroit, Michigan)

Zhiming Zhang (Department of Mathematics, Wayne State University, Detroit, Michigan)

Abstract

In this paper, we propose explicit two-stage Runge-Kutta schemes of strong order one for solutions of stochastic differential equations driven by jump-diffusion processes. By using rooted trees, we obtain the convergence rate. Our numerical tests verify our theoretical results. Key words. Stochastic differential equation, numerical approximation, stochastic Runge-Kutta methods, jump-diffusion.

Keywords

stochastic differential equation, numerical approximation, stochastic Runge-Kutta methods, jump-diffusion

2010 Mathematics Subject Classification

60H30, 65C30

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