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February 2021 On the weak convergence rate of an exponential Euler scheme for SDEs governed by coefficients with superlinear growth
Mireille Bossy, Jean-François Jabir, Kerlyns Martínez
Bernoulli 27(1): 312-347 (February 2021). DOI: 10.3150/20-BEJ1241

Abstract

We consider the problem of designing robust numerical integration scheme of the solution of a one-dimensional SDE with non-globally Lipschitz drift and diffusion coefficients behaving as $x^{\alpha }$, with $\alpha >1$. We propose an (semi-explicit) exponential-Euler scheme for which we obtain a theoretical convergence rate for the weak error. To this aim, we analyze the $C^{1,4}$ regularity of the solution of the associated backward Kolmogorov PDE using its Feynman–Kac representation and the flow derivative of the involved processes. Under some suitable hypotheses on the parameters of the model, we prove a rate of weak convergence of order one for the proposed exponential Euler scheme, and illustrate it with some numerical experiments.

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Mireille Bossy. Jean-François Jabir. Kerlyns Martínez. "On the weak convergence rate of an exponential Euler scheme for SDEs governed by coefficients with superlinear growth." Bernoulli 27 (1) 312 - 347, February 2021. https://doi.org/10.3150/20-BEJ1241

Information

Received: 1 September 2019; Revised: 1 April 2020; Published: February 2021
First available in Project Euclid: 20 November 2020

zbMATH: 07282853
MathSciNet: MR4177372
Digital Object Identifier: 10.3150/20-BEJ1241

Keywords: Feynman–Kac representation , Numerical scheme , polynomial coefficients , rate of convergence , Stochastic differential equation , weak convergence

Rights: Copyright © 2021 Bernoulli Society for Mathematical Statistics and Probability

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Vol.27 • No. 1 • February 2021
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