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Theory of Probability and Mathematical Statistics
Theory of Probability and Mathematical Statistics
ISSN 1547-7363(online) ISSN 0094-9000(print)

 

Dynamic random evolutions on increasing time intervals


Author: V. S. Koroliuk
Translated by: N. Semenov
Original publication: Teoriya Imovirnostei ta Matematichna Statistika, tom 85 (2011).
Journal: Theor. Probability and Math. Statist. 85 (2012), 83-91
MSC (2000): Primary 60J55, 60B10, 60F17, 60K10; Secondary 60G46, 60G60
Published electronically: January 14, 2013
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Abstract | References | Similar Articles | Additional Information

Abstract: We consider the following three main limit theorems for random evolutions: the averaging scheme, diffusion approximation, and asymptotic behavior of large deviations.

We study the asymptotic behavior of random evolutions in increasing time intervals in the scheme of series with a small parameter by using solutions of the singular perturbation problem for reducible-invertible operators.


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Additional Information

V. S. Koroliuk
Affiliation: Institute of Mathematics, National Academy of Science of Ukraine, Tereshchenkivs’ka Street, 3, Kyiv 01601, Ukraine
Email: korol@imath.kiev.ua

DOI: http://dx.doi.org/10.1090/S0094-9000-2013-00876-X
PII: S 0094-9000(2013)00876-X
Keywords: Dynamic random evolution, averaging, diffusion approximation, large deviations, exponential nonlinear operator
Received by editor(s): May 10, 2011
Published electronically: January 14, 2013
Article copyright: © Copyright 2013 American Mathematical Society