Strong convergence of semi-implicit split-step methods for SDE with locally Lipschitz coefficients

İzgi B., Cetin C.

COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION, vol.94, 2021 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 94
  • Publication Date: 2021
  • Doi Number: 10.1016/j.cnsns.2020.105574
  • Journal Name: COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, Aerospace Database, Aquatic Science & Fisheries Abstracts (ASFA), Communication Abstracts, Compendex, INSPEC, Metadex, zbMATH, Civil Engineering Abstracts
  • Istanbul Technical University Affiliated: Yes

Abstract

We discuss mean-square strong convergence properties for numerical solutions of a class of stochastic differential equations with super-linear drift terms using semi-implicit split step methods. Under a one-sided Lipschitz condition on the drift term and a global Lipschitz condition on the diffusion term, we show that these numerical procedures yield the usual strong convergence rate of 1/2. We also present simulation-based applications including stochastic logistic growth equations, and compare their empirical convergence with some alternate methods. (C) 2020 Elsevier B.V. All rights reserved.