Large Deviations for Random Evolutions in the Scheme of Asymptotically Small Diffusion

Volodymyr S. Korolyuk () and Igor V. Samoilenko ()
Additional contact information
Volodymyr S. Korolyuk: Institute of Mathematics NASU
Igor V. Samoilenko: Institute of Mathematics NASU

A chapter in Modern Stochastics and Applications, 2014, pp 203-219 from Springer

Abstract: Abstract The theory of large deviations deals with the asymptotic estimations for probabilities of rare events. The method, used in majority of classical works, is based on the change of measure and application of the variational formula to the cumulant of the process under study. Here the large deviations problem is considered for random evolutions in the scheme of asymptotically small diffusion. The method of asymptotic analysis for the exponential generator of the Markov process is used. The limit exponential generators are calculated for random evolution with the ergodic Markov switching (Sect. 3) and with the split-and-double merging switching Markov process (Sect. 4). The method proposed here may have applications for the finite dimensional models arising in the theory of random evolutions in R d , queuing theory, etc.

Keywords: Random Evolution; Large Deviation Problem; Markov Switching Process; Exponential Generator; Markov Chain (search for similar items in EconPapers)
Date: 2014
References: Add references at CitEc
Citations:

There are no downloads for this item, see the EconPapers FAQ for hints about obtaining it.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:spochp:978-3-319-03512-3_12

Ordering information: This item can be ordered from
http://www.springer.com/9783319035123

DOI: 10.1007/978-3-319-03512-3_12

Access Statistics for this chapter

More chapters in Springer Optimization and Its Applications from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().