On the strong convergence rate for the Euler–Maruyama scheme of one-dimensional SDEs with irregular diffusion coefficient and local time

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Abstract

The strong rate of convergence for the Euler–Maruyama scheme of stochastic differential equations (SDEs) driven by a Brownian motion with Hölder continuous diffusion coefficient or irregular drift coefficient have been widely studied. In the case of irregular diffusion coefficient, however, there are few studies. In this article, under Le Gall's condition on the diffusion coefficient, which leads to conclude the pathwise uniqueness for SDEs, we provide the same result on the strong rate of convergence as in the case of 1/2-Hölder continuous diffusion coefficient. The idea of the proof is to use a version of Avikainen's inequality. As an application, we introduce a numerical scheme for SDEs with local time.

Original languageEnglish
Article number101695
JournalJournal of Complexity
DOIs
Publication statusAccepted/In press - 2022

Keywords

  • Avikainen's inequality
  • Euler–Maruyama scheme
  • Irregular diffusion coefficient
  • Rate of convergence
  • SDEs with local time
  • Stochastic differential equation

ASJC Scopus subject areas

  • Algebra and Number Theory
  • Statistics and Probability
  • Numerical Analysis
  • Mathematics(all)
  • Control and Optimization
  • Applied Mathematics

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