Heriot-Watt Mathematics Report Series
HWM09-8, 24 Sep 2009
Stochastic Runge-Kutta methods for Ito stochastic differential equations of jump type
E Buckwar and M G Riedler
Abstract
In this paper we consider stochastic Runge-Kutta methods for stochastic differential equations of jump type. We present a study of their convergence properties for problems with small multiplicative noise. We are concerned with two classes of Runge-Kutta methods. Firstly, we analyse schemes where the drift is approximated by a Runge-Kutta ansatz and the diffusion and jump part by a Maruyama term and secondly we discuss improved methods where mixed stochastic integrals are incorporated in the approximation of the next time step as well as the
stage values of the Runge-Kutta ansatz for the drift. We present results when the implicit stochastic equations for the stage values are uniquely solvable. Finally, simulation results illustrate the theoretical findings.
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Full text: http://www.ma.hw.ac.uk/~mgr2/jsode_srk_preprint.pdf
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