Compensated stochastic theta methods for stochastic differential equations with jumps

Authors:
Xiaojie Wang;Siqing Gan
Affiliations:
School of Mathematical Sciences and Computing Technology, Central South University, Changsha 410075, Hunan, China;School of Mathematical Sciences and Computing Technology, Central South University, Changsha 410075, Hunan, China
Venue:
Applied Numerical Mathematics
Year:
2010

Citing 5
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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An Algorithmic Introduction to Numerical Simulation of Stochastic Differential Equations

SIAM Review
Numerical methods for nonlinear stochastic differential equations with jumps

Numerische Mathematik
Asymptotic Stability of a Jump-Diffusion Equation and Its Numerical Approximation

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

Journal of Computational and Applied Mathematics
Asymptotic stability of balanced methods for stochastic jump-diffusion differential equations

Journal of Computational and Applied Mathematics

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Abstract

In this paper, a family of compensated stochastic theta methods (CSTM), as opposed to stochastic theta methods (STM) are proposed after the introduction of a compensated Poisson process. These methods are justified to have a strong convergence order of 1/2. Further we investigate mean-square stability of the proposed methods. For a linear test equation, we show that an extension of the deterministic A-stability property holds for CSTM, if and only if 1/2=