Polynomial and exponential stability of θ-EM approximations to a class of stochastic differential equations

2014/07/06 by Yunjiao Hu, Hu, Yunjiao, Guangqiang Lan +3
Economics, Econometrics and Finance · Mathematics · #60H10 #65C30 #FOS: Mathematics #Fractional Differential Equations Solutions #Mathematical functions and polynomials #Numerical Analysis (math.NA) #Stochastic processes and financial applications

paper · pdf · doi:10.48550/arxiv.1407.1486

openalex publication_date 2014/07/06 · openalex created_date 2016/09/16 · openalex updated_date 2026/07/28

Abstract

Both the mean square polynomial stability and exponential stability of θ Euler-Maruyama approximation solutions of stochastic differential equations will be investigated for each 0≤θ≤ 1 by using an auxiliary function F (see the following definition (2.3)). Sufficient conditions are obtained to ensure the polynomial and exponential stability of the numerical approximations. The results in Liu et al [12] will be improved and generalized to more general cases. Several examples and non stability results are presented to support our conclusions.

Citations

• V-Integrability, Asymptotic Stability And Comparison Theorem of Explicit Numerical Schemes for SDEs
• Mean Square Polynomial Stability of Numerical Solutions to a Class of Stochastic Differential Equations

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