Large deviations for renewal processes

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Abstract

Let {Xn, n ≥1} be a sequence of identically distributed real random variables with EX1 = μ > 0. Define Snni=1Xi and Nα(t) = inf{n≥1;Sn>nαt}, where t>0, α∈[0, 1) and the infimum o f the empty set is defined to be +∞. Let Pα,t be the distribution of Nα(t)/t1/(1-α), t > 0. In this paper, we establish the large deviation principle for {Pα, t; t > 0} when {Xn; n≥ 1 } is a sequence of i.i.d. random variables or, more generally, an exchangeable sequence.

Original languageEnglish (US)
Pages (from-to)57-71
Number of pages15
JournalStochastic Processes and their Applications
Volume50
Issue number1
DOIs
StatePublished - 1994

Bibliographical note

Funding Information:
Corres[>or&nce to: Dr. Jiang Tiefeng, Department of Mathematics, Jilin University, Changchun Province. People’s Republic of China. Research supported by the National Natural Science Foundation of China.

Keywords

  • exchangeable random variables
  • large deviations
  • rate function
  • renewal processes

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