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Veretennikov, A. Yu.; Kulik, A. M.

Diffusion approximation of systems with weakly ergodic Markov perturbations. I. (English. Ukrainian original) Zbl 1337.60197

Theory Probab. Math. Stat. 87, 13-29 (2013); translation from Teor. Jmovirn. Mat. Stat. 87, 12-27 (2012).
Summary: Diffusion approximation type results are obtained for a system perturbed by a Markov process whose transition probabilities converge to the invariant distribution nonuniformly with respect to the initial value. In general, the mode of convergence is weaker than the total variation convergence.

Cited in 1 Review
Cited in 1 Document

MSC:

60J60 Diffusion processes
60F05 Central limit and other weak theorems
60H10 Stochastic ordinary differential equations (aspects of stochastic analysis)
60J10 Markov chains (discrete-time Markov processes on discrete state spaces)

Keywords:

diffusion approximation; weakly ergodic Markov perturbations; corrector; extended potential

Citations:

Zbl 1337.60198
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Full Text: DOI

References:

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