Bernoulli

  • Bernoulli
  • Volume 23, Number 2 (2017), 927-950.

Multilevel path simulation for weak approximation schemes with application to Lévy-driven SDEs

Denis Belomestny and Tigran Nagapetyan

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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.

Article information

Source
Bernoulli, Volume 23, Number 2 (2017), 927-950.

Dates
Received: September 2014
Revised: August 2015
First available in Project Euclid: 4 February 2017

Permanent link to this document
https://projecteuclid.org/euclid.bj/1486177388

Digital Object Identifier
doi:10.3150/15-BEJ764

Mathematical Reviews number (MathSciNet)
MR3606755

Zentralblatt MATH identifier
06701615

Keywords
Lévy-driven stochastic differential equations multilevel Monte Carlo weak approximation schemes

Citation

Belomestny, Denis; Nagapetyan, Tigran. Multilevel path simulation for weak approximation schemes with application to Lévy-driven SDEs. Bernoulli 23 (2017), no. 2, 927--950. doi:10.3150/15-BEJ764. https://projecteuclid.org/euclid.bj/1486177388


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