Open Access
August 2017 Unbiased simulation of stochastic differential equations using parametrix expansions
Patrik Andersson, Arturo Kohatsu-Higa
Bernoulli 23(3): 2028-2057 (August 2017). DOI: 10.3150/16-BEJ803

Abstract

In this article, we consider an unbiased simulation method for multidimensional diffusions based on the parametrix method for solving partial differential equations with Hölder continuous coefficients. This Monte Carlo method which is based on an Euler scheme with random time steps, can be considered as an infinite dimensional extension of the Multilevel Monte Carlo method for solutions of stochastic differential equations with Hölder continuous coefficients. In particular, we study the properties of the variance of the proposed method. In most cases, the method has infinite variance and therefore we propose an importance sampling method to resolve this issue.

Citation

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Patrik Andersson. Arturo Kohatsu-Higa. "Unbiased simulation of stochastic differential equations using parametrix expansions." Bernoulli 23 (3) 2028 - 2057, August 2017. https://doi.org/10.3150/16-BEJ803

Information

Received: 1 September 2014; Revised: 1 September 2015; Published: August 2017
First available in Project Euclid: 17 March 2017

zbMATH: 06714326
MathSciNet: MR3624885
Digital Object Identifier: 10.3150/16-BEJ803

Keywords: importance sampling , Monte Carlo method , multidimensional diffusion , Parametrix

Rights: Copyright © 2017 Bernoulli Society for Mathematical Statistics and Probability

Vol.23 • No. 3 • August 2017
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