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

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 η/2 , where h is the time step of the scheme, η being the Hölder exponent of the diffusion coefficient.
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https://hal.archives-ouvertes.fr/hal-01373949
Contributor : Noufel Frikha <>
Submitted on : Thursday, September 29, 2016 - 2:25:20 PM
Last modification on : Friday, March 27, 2020 - 3:05:43 AM

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  • HAL Id : hal-01373949, version 1

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N Frikha. ON THE WEAK APPROXIMATION OF A SKEW DIFFUSION BY AN EULER-TYPE SCHEME. 2016. ⟨hal-01373949⟩

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