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S. A. Klokov, A. Yu. Veretennikov

On mixing and convergence rates for a family of Markov processes approximating SDEs

We study a class of Markov processes of the type

which are approximations of the SDE:

where F : R^d → R^d is a Borel function, and (ξ_n ) are i.i.d. random variables with zero mean. Upper estimates for β-mixing and convergence rates in the range from the weakest polynomial to exponential to a (unique) invariant measure are established on the base of the stochastic calculus of variations under certain assumptions on smoothness of F, on the density of ξ_n , and under some recurrence conditions.

Random Operators and Stochastic Equations, Walter de Gruyter

Print ISSN: 0926-6364
Volume: 14, 04/2006
Pages: 103 - 126

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