Split-step forward methods for stochastic differential equations

Authors:
Peng Wang;Yong Li
Affiliations:
Institute of Mathematics, Jilin University, Changchun 130012, PR China;College of Mathematics, Jilin University, Changchun 130012, PR China
Venue:
Journal of Computational and Applied Mathematics
Year:
2010

Citing 10
Cited 1

Stability Analysis of Numerical Schemes for Stochastic Differential Equations

SIAM Journal on Numerical Analysis
Balanced Implicit Methods for Stiff Stochastic Systems

SIAM Journal on Numerical Analysis
A General Implicit Splitting for Stabilizing Numerical Simulations of Itô Stochastic Differential Equations

SIAM Journal on Numerical Analysis
Implicit Taylor methods for stiff stochastic differential equations

Applied Numerical Mathematics
The composite Euler method for stiff stochastic differential equations

Journal of Computational and Applied Mathematics
Mean-Square and Asymptotic Stability of the Stochastic Theta Method

SIAM Journal on Numerical Analysis
Strong Convergence of Euler-Type Methods for Nonlinear Stochastic Differential Equations

SIAM Journal on Numerical Analysis
An Algorithmic Introduction to Numerical Simulation of Stochastic Differential Equations

SIAM Review
Three-stage stochastic Runge-Kutta methods for stochastic differential equations

Journal of Computational and Applied Mathematics
Split-step backward balanced Milstein methods for stiff stochastic systems

Applied Numerical Mathematics

Split-step θ-method for stochastic delay differential equations

Applied Numerical Mathematics

Quantified Score

Hi-index	7.29

Visualization

Abstract

In this paper we discuss split-step forward methods for solving Ito stochastic differential equations (SDEs). Eight fully explicit methods, the drifting split-step Euler (DRSSE) method, the diffused split-step Euler (DISSE) method and the three-stage Milstein (TSM 1a-TSM 1f) methods, are constructed based on Euler-Maruyama method and Milstein method, respectively, in this paper. Their order of strong convergence is proved. The analysis of stability shows that the mean-square stability properties of the methods derived in this paper are improved on the original methods. The numerical results show the effectiveness of these methods in the pathwise approximation of Ito SDEs.