## 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

#### 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