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

Olivier Menoukeu Pamen and Dai Taguchi

Stochastic Processes and their Applications, 2017, vol. 127, issue 8, 2542-2559

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.

Keywords: Euler–Maruyama approximation; Strong approximation; Rate of convergence; Hölder continuous drift; Truncated symmetric α-stable (search for similar items in EconPapers)
Date: 2017
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Citations: View citations in EconPapers (6)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:spapps:v:127:y:2017:i:8:p:2542-2559

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DOI: 10.1016/j.spa.2016.11.008

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