Strong rate of convergence for the Euler–Maruyama approximation of SDEs with Hölder continuous drift coefficient

Olivier Menoukeu Pamen, Dai Taguchi

Research output: Contribution to journalArticlepeer-review

9 Citations (Scopus)

Abstract

In this paper, we consider a numerical approximation of the stochastic differential equation (SDE) Xt=x0+∫0tb(s,Xs)ds+Lt,x0∈Rd,t∈[0,T], where the drift coefficient b:[0,T]×Rd→Rd is Hölder continuous in both time and space variables and the noise L=(Lt)0≤t≤T is a d-dimensional Lévy process. We provide the rate of convergence for the Euler–Maruyama approximation when L is a Wiener process or a truncated symmetric α-stable process with α∈(1,2). Our technique is based on the regularity of the solution to the associated Kolmogorov equation.

Original languageEnglish
Pages (from-to)2542-2559
Number of pages18
JournalStochastic Processes and their Applications
Volume127
Issue number8
DOIs
Publication statusPublished - Aug 2017
Externally publishedYes

Keywords

  • Euler–Maruyama approximation
  • Hölder continuous drift
  • Rate of convergence
  • Strong approximation
  • Truncated symmetric α-stable

ASJC Scopus subject areas

  • Statistics and Probability
  • Modelling and Simulation
  • Applied Mathematics

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