Exponential mean square stability of numerical methods for systems of stochastic differential equations

Authors:
Chengming Huang
Affiliations:
-
Venue:
Journal of Computational and Applied Mathematics
Year:
2012

Citing 7
Cited 2

Stability Analysis of Numerical Schemes for Stochastic Differential Equations

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Mean-Square and Asymptotic Stability of the Stochastic Theta Method

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Strong Convergence of Euler-Type Methods for Nonlinear Stochastic Differential Equations

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Numerical methods for nonlinear stochastic differential equations with jumps

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Almost Sure and Moment Exponential Stability in the Numerical Simulation of Stochastic Differential Equations

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Compensated stochastic theta methods for stochastic differential equations with jumps

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Towards a Systematic Linear Stability Analysis of Numerical Methods for Systems of Stochastic Differential Equations

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Choice of θ and mean-square exponential stability in the stochastic theta method of stochastic differential equations

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Mean square stability and dissipativity of two classes of theta-methods for systems of stochastic delay differential equations

Journal of Computational and Applied Mathematics

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Abstract

This paper is concerned with exponential mean square stability of the classical stochastic theta method and the so called split-step theta method for stochastic systems. First, we consider linear autonomous systems. Under a sufficient and necessary condition for exponential mean square stability of the exact solution, it is proved that the two classes of theta methods with @q=0.5 are exponentially mean square stable for all positive step sizes and the methods with @q0.5 still unconditionally preserves the exponential mean square stability of the underlying systems, but the stochastic theta method does not have this property. Finally, we consider stochastic differential equations with jumps. Some similar results are derived.