Open Access
August 2018 On the weak approximation of a skew diffusion by an Euler-type scheme
Noufel Frikha
Bernoulli 24(3): 1653-1691 (August 2018). DOI: 10.3150/16-BEJ909


We study the weak approximation error of a skew diffusion with bounded measurable drift and Hölder diffusion coefficient by an Euler-type scheme, which consists of iteratively simulating skew Brownian motions with constant drift. We first establish two sided Gaussian bounds for the density of this approximation scheme. Then, a bound for the difference between the densities of the skew diffusion and its Euler approximation is obtained. Notably, the weak approximation error is shown to be of order $h^{\eta/2}$, where $h$ is the time step of the scheme, $\eta$ being the Hölder exponent of the diffusion coefficient.


Download Citation

Noufel Frikha. "On the weak approximation of a skew diffusion by an Euler-type scheme." Bernoulli 24 (3) 1653 - 1691, August 2018.


Received: 1 February 2016; Revised: 1 October 2016; Published: August 2018
First available in Project Euclid: 2 February 2018

zbMATH: 06839249
MathSciNet: MR3757512
Digital Object Identifier: 10.3150/16-BEJ909

Keywords: Euler scheme , Gaussian bounds , skew diffusion , weak error

Rights: Copyright © 2018 Bernoulli Society for Mathematical Statistics and Probability

Vol.24 • No. 3 • August 2018
Back to Top