Fluctuations of a stochastic system under an asymptotic diffusive perturbation

Authors:
S. A. Semenyuk;Ya. M. Chabanyuk
Affiliations:
Institute of Applied Mathematics and Fundamental Sciences of National University "Lvivs'ka Politekhnika", Lvov, Ukraine;Institute of Applied Mathematics and Fundamental Sciences of National University "Lvivs'ka Politekhnika", Lvov, Ukraine
Venue:
Cybernetics and Systems Analysis
Year:
2008

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Abstract

A stochastic singularly perturbed system is considered. Sufficient conditions of the asymptotic normality are obtained for the dynamic system in the vicinity of its equilibrium point. To this end, a solution to the singular perturbation problem is constructed for an asymptotic representation of the generator of a Markov renewal process.