Stationary distribution of the Milstein scheme for stochastic differential delay equations with first-order convergence

Shuaibin Gao, Xiaotong Li and Zhuoqi Liu

Applied Mathematics and Computation, 2023, vol. 458, issue C

Abstract: This paper focuses on the stationary distribution of the Milstein scheme for stochastic differential delay equations. The numerical segment process is constructed, which is proved to be a time homogeneous Markov process. We show that this numerical segment process admits a unique numerical stationary distribution. Then we reveal that the distribution of numerical segment process converges exponentially to the underlying one in the Wasserstein metric. Moreover, the first-order convergence of numerical stationary distribution to exact stationary distribution is presented. Finally, abundant numerical experiments confirm the reliability of theoretical findings.

Keywords: The Milstein scheme; Stochastic differential delay equations; Stationary distribution; Markov process (search for similar items in EconPapers)
Date: 2023
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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:458:y:2023:i:c:s0096300323003934

DOI: 10.1016/j.amc.2023.128224

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