The Truncated Euler-Maruyama Method for Stochastic Differential Delay Equations

Abstract

The numerical solutions of stochastic differential delay equations (SDDEs) under the generalized Khasminskii-type condition were discussed by Mao [15], and the theory there showed that the Euler-Maruyama (EM) numerical solutions converge to the true solutions in probability. However, there is so far no result on the strong convergence (namely in L^p) of the numerical solutions for the SDDEs under this generalized condition. In this paper, we will use the truncated EM method developed by Mao [16] to study the strong convergence of the numerical solutions for the SDDEs under the generalized Khasminskii-type condition.

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• Delay stochastic interest rate model with jump and strong convergence in Monte Carlo simulations
• Equivalence of pth moment stability between stochastic differential delay equations and their numerical methods
• The Strong Convergence and Stability of Explicit Approximations for Nonlinear Stochastic Delay Differential Equations
• The truncated EM method for stochastic differential delay equations with variable delay