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Large deviations for renewal processes

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  • Tiefeng, Jiang

Abstract

Let {Xn, n [greater-or-equal, slanted]1} be a sequence of identically distributed real random variables with EX1 = [mu] > 0. Define Sn=[Sigma]ni=1Xi and N[alpha](t) = inf{n[greater-or-equal, slanted]1;Sn>n[alpha]t}, where t>0, [alpha][set membership, variant][0, 1) and the infimum o f the empty set is defined to be +[infinity]. Let P[alpha],t be the distribution of N[alpha](t)/t1/(1-[alpha]), t> 0. In this paper, we establish the large deviation principle for {P[alpha], t; t> 0} when {Xn; n[greater-or-equal, slanted] 1 } is a sequence of i.i.d. random variables or, more generally, an exchangeable sequence.

Suggested Citation

  • Tiefeng, Jiang, 1994. "Large deviations for renewal processes," Stochastic Processes and their Applications, Elsevier, vol. 50(1), pages 57-71, March.
    • Handle: RePEc:eee:spapps:v:50:y:1994:i:1:p:57-71
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    Cited by:

    1. Cattiaux, Patrick & Colombani, Laetitia & Costa, Manon, 2023. "Asymptotic deviation bounds for cumulative processes," Stochastic Processes and their Applications, Elsevier, vol. 163(C), pages 85-105.
    2. Jeffrey Collamore & Andrea Höing, 2007. "Small-time ruin for a financial process modulated by a Harris recurrent Markov chain," Finance and Stochastics, Springer, vol. 11(3), pages 299-322, July.

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