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May 2017 Multilevel path simulation for weak approximation schemes with application to Lévy-driven SDEs
Denis Belomestny, Tigran Nagapetyan
Bernoulli 23(2): 927-950 (May 2017). DOI: 10.3150/15-BEJ764

Abstract

In this paper, we discuss the possibility of using multilevel Monte Carlo (MLMC) approach for weak approximation schemes. It turns out that by means of a simple coupling between consecutive time discretisation levels, one can achieve the same complexity gain as under the presence of a strong convergence. We exemplify this general idea in the case of weak Euler schemes for Lévy-driven stochastic differential equations. The numerical performance of the new “weak” MLMC method is illustrated by several numerical examples.

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Denis Belomestny. Tigran Nagapetyan. "Multilevel path simulation for weak approximation schemes with application to Lévy-driven SDEs." Bernoulli 23 (2) 927 - 950, May 2017. https://doi.org/10.3150/15-BEJ764

Information

Received: 1 September 2014; Revised: 1 August 2015; Published: May 2017
First available in Project Euclid: 4 February 2017

zbMATH: 06701615
MathSciNet: MR3606755
Digital Object Identifier: 10.3150/15-BEJ764

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

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Vol.23 • No. 2 • May 2017
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