Dynamic random evolutions on increasing time intervals
Author:
V. S. Koroliuk
Translated by:
N. Semenov
Journal:
Theor. Probability and Math. Statist. 85 (2012), 83-91
MSC (2000):
Primary 60J55, 60B10, 60F17, 60K10; Secondary 60G46, 60G60
DOI:
https://doi.org/10.1090/S0094-9000-2013-00876-X
Published electronically:
January 14, 2013
MathSciNet review:
2933705
Full-text PDF Free Access
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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.
References
- Vladimir S. Koroliuk and Nikolaos Limnios, Stochastic systems in merging phase space, World Scientific Publishing Co. Pte. Ltd., Hackensack, NJ, 2005. MR 2205562
- Vladimir S. Korolyuk and Vladimir V. Korolyuk, Stochastic models of systems, Mathematics and its Applications, vol. 469, Kluwer Academic Publishers, Dordrecht, 1999. MR 1753470
- Stewart N. Ethier and Thomas G. Kurtz, Markov processes, Wiley Series in Probability and Mathematical Statistics: Probability and Mathematical Statistics, John Wiley & Sons, Inc., New York, 1986. Characterization and convergence. MR 838085
- Jin Feng and Thomas G. Kurtz, Large deviations for stochastic processes, Mathematical Surveys and Monographs, vol. 131, American Mathematical Society, Providence, RI, 2006. MR 2260560
- M. I. Freidlin and A. D. Wentzell, Random perturbations of dynamical systems, 2nd ed., Grundlehren der Mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences], vol. 260, Springer-Verlag, New York, 1998. Translated from the 1979 Russian original by Joseph Szücs. MR 1652127
- William Feller, An introduction to probability theory and its applications. Vol. II, John Wiley & Sons, Inc., New York-London-Sydney, 1966. MR 0210154
- I. I. Gikhman and A. V. Skorokhod, Introduction to the theory of random processes, Dover Publications, Inc., Mineola, NY, 1996. Translated from the 1965 Russian original; Reprint of the 1969 English translation; With a preface by Warren M. Hirsch. MR 1435501
References
- V. S. Koroliuk and N. Limnios, Stochastic Systems in Merging Phase Space, World Scientific Publishing Co. Pte. Ltd., Hackensack, NJ, 2005. MR 2205562 (2007a:60004)
- V. S. Korolyuk and V. V. Korolyuk, Stochastic Models of Systems, Kluwer Academic Publishers, Dordrecht, 1999. MR 1753470 (2002b:60169)
- S. N. Ethier and T. G. Kurtz, Markov Processes. Characterization and Convergence, John Wiley & Sons, Inc., New York, 1986. MR 838085 (88a:60130)
- J. Feng and T. G. Kurtz, Large Deviations for Stochastic Processes, American Mathematical Society, Providence, RI, 2006. MR 2260560 (2009g:60034)
- M. J. Freidlin and A. M. Wentzel, Random Perturbation of Dynamical Systems, Springer Verlag, Berlin, 1998. MR 1652127 (99h:60128)
- W. Feller, An Introduction to Probability Theory and Its Applications, Vol. II, John Wiley & Sons Inc., New York–London–Sydney, 1966. MR 0210154 (35:1048)
- I. I. Gikhman and A. V. Skorokhod, Introduction to the Theory of Random Processes, “Nauka”, Moscow, 1977; English transl., Dover Publications, Inc., Mineola, NY, 1996. MR 1435501 (97j:60001)
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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
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
