On the Weak Approximation of a Skew Diffusion by an Euler-type Scheme
نویسندگان
چکیده
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, where h is the time step of the scheme, η being the Hölder exponent of the diffusion coefficient. 1991 Mathematics Subject Classification. 60H35,65C30,65C05. September 30, 2016.
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