Remote Access Theory of Probability and Mathematical Statistics

Theory of Probability and Mathematical Statistics

ISSN 1547-7363(online) ISSN 0094-9000(print)

Request Permissions   Purchase Content 


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
Full-text PDF

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.

References [Enhancements On Off] (What's this?)

  • 1. Vladimir S. Koroliuk and Nikolaos Limnios, Stochastic systems in merging phase space, World Scientific Publishing Co. Pte. Ltd., Hackensack, NJ, 2005. MR 2205562
  • 2. Vladimir S. Korolyuk and Vladimir V. Korolyuk, Stochastic models of systems, Mathematics and its Applications, vol. 469, Kluwer Academic Publishers, Dordrecht, 1999. MR 1753470
  • 3. 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
  • 4. 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
  • 5. 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
  • 6. William Feller, An introduction to probability theory and its applications. Vol. II, John Wiley & Sons, Inc., New York-London-Sydney, 1966. MR 0210154
  • 7. 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

Similar Articles

Retrieve articles in Theory of Probability and Mathematical Statistics with MSC (2000): 60J55, 60B10, 60F17, 60K10, 60G46, 60G60

Retrieve articles in all journals with MSC (2000): 60J55, 60B10, 60F17, 60K10, 60G46, 60G60

Additional Information

V. S. Koroliuk
Affiliation: Institute of Mathematics, National Academy of Science of Ukraine, Tereshchenkivs’ka Street, 3, Kyiv 01601, Ukraine

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