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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

Topics:
1991 Mathematics Subject Classification 60H35, 65C30, 65C05, [
INFO.INFO-MO
]
Computer Science [cs]/Modeling and Simulation, [
MATH.MATH-PR
]
Mathematics [math]/Probability [math.PR]

Publisher: HAL CCSD

Year: 2016

OAI identifier:
oai:HAL:hal-01373949v1

Provided by:
Hal-Diderot

Downloaded from
https://hal.archives-ouvertes.fr/hal-01373949/document

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