Approximations of Euler-Maruyama type for stochastic differential equations with Markovian switching, under non-Lipschitz conditions

Authors:
Xuerong Mao;Chenggui Yuan;G. Yin
Affiliations:
Department of Statistics and Modelling Science, University of Strathclyde, Glasgow G1 1XH, UK;Department of Mathematics, University of Wales Swansea, Swansea SA2 8PP, UK;Department of Mathematics, Wayne State University, Detroit, MI 48202, USA
Venue:
Journal of Computational and Applied Mathematics
Year:
2007

Citing 3
Cited 1

Necessary and sufficient condition for robust stability and stabilizability of continuous-time linear systems with Markovian jumps

Journal of Optimization Theory and Applications
Strong Convergence of Euler-Type Methods for Nonlinear Stochastic Differential Equations

SIAM Journal on Numerical Analysis
Convergence of the Euler-Maruyama method for stochastic differential equations with Markovian switching

Mathematics and Computers in Simulation

Strong convergence and stability of implicit numerical methods for stochastic differential equations with non-globally Lipschitz continuous coefficients

Journal of Computational and Applied Mathematics

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Abstract

We develop the Euler-Maruyama scheme for a class of stochastic differential equations with Markovian switching (SDEwMSs) under non-Lipschitz conditions. Both L^1 and L^2-convergence are discussed under different non-Lipschitz conditions. To overcome the mathematical difficulties arisen from the Markovian switching as well as the non-Lipschitz coefficients, several new analytical techniques have been developed in this paper which should prove to be very useful in the numerical analysis of stochastic systems.