Abstract
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.
Citation
Noufel Frikha. "On the weak approximation of a skew diffusion by an Euler-type scheme." Bernoulli 24 (3) 1653 - 1691, August 2018. https://doi.org/10.3150/16-BEJ909
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