Convergence and stability of the split-step θ-method for stochastic differential equations

Authors:
Xiaohua Ding;Qiang Ma;Lei Zhang
Affiliations:
-;-;-
Venue:
Computers & Mathematics with Applications
Year:
2010

Citing 8
Cited 2

Real and complex analysis, 3rd ed.

Real and complex analysis, 3rd ed.
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

SIAM Journal on Numerical Analysis
Mean-square convergence of stochastic multi-step methods with variable step-size

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Mean-square stability of second-order Runge-Kutta methods for multi-dimensional linear stochastic differential systems

Journal of Computational and Applied Mathematics
Three-stage stochastic Runge-Kutta methods for stochastic differential equations

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Mean-square stability of second-order Runge-Kutta methods for 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
Split-step θ-method for stochastic delay differential equations

Applied Numerical Mathematics

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Abstract

In this paper, we construct a new split-step method for solving stochastic differential equations, namely the split-step @q-method. Under Lipschitz and linear growth conditions, we establish a mean-square convergence theory of split-step @q-approximate solutions. Moreover, the mean-square stability of the method for a linear test equation with real parameters is considered and the real mean-square stability region is plotted. Finally, numerical results are presented to demonstrate the efficiency of the split-step @q-method.