Rate of convergence for numerical solutions to SFDEs with jumps

2009/06/18 by Jianhai Bao, Xuerong Mao, Bao, Jianhai +3
Economics, Econometrics and Finance · Mathematics · #65C30 #65L20 #Differential Equations and Numerical Methods #FOS: Mathematics #Numerical Analysis (math.NA) #Numerical methods for differential equations #Probability (math.PR) #Stochastic processes and financial applications

paper · pdf · doi:10.48550/arxiv.0906.3455

openalex publication_date 2009/06/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01

Abstract

In this paper, we are interested in the numerical solutions of stochastic functional differential equations (SFDEs) with \it jumps. Under the global Lipschitz condition, we show that the pth moment convergence of the Euler-Maruyama (EM) numerical solutions to SFDEs with jumps has order 1/p for any p≥ 2. This is significantly different from the case of SFDEs without jumps where the order is 1/2 for any p≥ 2. It is therefore best to use the mean-square convergence for SFDEs with jumps. Consequently, under the local Lipschitz condition, we reveal that the order of the mean-square convergence is close to 1/2, provided that the local Lipschitz constants, valid on balls of radius j, do not grow faster than log j.

Citations

• Numerical methods for nonlinear stochastic differential equations with jumps

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