Ukrainian Mathematical Journal

, Volume 57, Issue 9, pp 1442–1465 | Cite as

Stochastic Systems with Averaging in the Scheme of Diffusion Approximation

  • V. S. Korolyuk


We propose a system approach to the asymptotic analysis of stochastic systems in the scheme of series with averaging and diffusion approximation. Stochastic systems are defined by Markov processes with locally independent increments in a Euclidean space with random switchings that are described by jump Markov and semi-Markov processes. We use the asymptotic analysis of Markov and semi-Markov random evolutions. We construct the diffusion approximation using the asymptotic decomposition of generating operators and solutions of problems of singular perturbation for reducibly inverse operators.


Euclidean Space System Approach Markov Process Generate Operator Asymptotic Analysis 
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Copyright information

© Springer Science+Business Media, Inc. 2005

Authors and Affiliations

  • V. S. Korolyuk
    • 1
  1. 1.Institute of MathematicsUkrainian Academy of SciencesKyivUkraine

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