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 (Journal Indexed in SCI) identifier identifier

  • Publication Type: Article / Article
  • Volume: 94
  • Publication Date: 2021
  • Doi Number: 10.1016/j.cnsns.2020.105574
  • Title of Journal : COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION

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.