Large deviations for processes with discontinuous statistics

2004/09/30 by Irina Ignatiouk-Robert · 2 citations
Business, Management and Accounting · Decision Sciences · Mathematics · #Advanced Queuing Theory Analysis #Markov Chains and Monte Carlo Methods #Probability and Risk Models #math.PR #msc:60F10 #msc:60J15 #msc:60K35

paper · pdf · doi:10.1214/009117905000000189

published as Annals of Probability 2005, Vol. 33, No. 4, 1479-1508 · Published at http://dx.doi.org/10.1214/009117905000000189 in the Annals of Probability (http://www.imstat.org/aop/) by the Institute of Mathematical Statistics (http://www.imstat.org)

openalex publication_date 2005/07/01 · arxiv created 2005/08/25 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

This paper is devoted to the problem of sample path large deviations for the Markov processes on ℝ+N having a constant but different transition mechanism on each boundary set x:xi=0 for i∉Λ, xi>0 for i∈Λ. The global sample path large deviation principle and an integral representation of the rate function are derived from local large deviation estimates. Our results complete the proof of Dupuis and Ellis of the sample path large deviation principle for Markov processes describing a general class of queueing networks.

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