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Article Dans Une Revue Bernoulli Année : 2018

ON THE WEAK APPROXIMATION OF A SKEW DIFFUSION BY AN EULER-TYPE SCHEME

Résumé

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 η/2 , where h is the time step of the scheme, η being the Hölder exponent of the diffusion coefficient.
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Dates et versions

hal-01373949 , version 1 (29-09-2016)

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N Frikha. ON THE WEAK APPROXIMATION OF A SKEW DIFFUSION BY AN EULER-TYPE SCHEME. Bernoulli, 2018, 24 (3), pp.1653-1691. ⟨10.3150/16-BEJ909⟩. ⟨hal-01373949⟩
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