An explicit approximation for super-linear stochastic functional differential equations

Xiaoyue Li, Xuerong Mao and Guoting Song

Stochastic Processes and their Applications, 2024, vol. 169, issue C

Abstract: Since it is difficult to implement implicit schemes on the infinite-dimensional space, we aim to develop the explicit numerical method for approximating super-linear stochastic functional differential equations (SFDEs). Precisely, borrowing the truncation idea and linear interpolation we propose an explicit truncated Euler–Maruyama (EM) scheme for SFDEs, and obtain the boundedness and convergence in Lp(p≥2). We also prove the convergence rate with 1/2 order. Different from some previous works (Mao, 2003; Zhang et al., 2018), we release the global Lipschitz restriction on the diffusion coefficient. Furthermore, we reveal that numerical solutions preserve the underlying exponential stability. Moreover, we give several examples to support our theory.

Keywords: Stochastic functional differential equation; Truncated Euler–Maruyama scheme; Boundedness; Strong convergence; Exponential stability (search for similar items in EconPapers)
Date: 2024
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DOI: 10.1016/j.spa.2023.104275

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