Large deviations for renewal processes

Jiang Tiefeng

Stochastic Processes and their Applications, 1994, vol. 50, issue 1, 57-71

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.

Keywords: renewal; processes; large; deviations; rate; function; exchangeable; random; variables (search for similar items in EconPapers)
Date: 1994
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Citations: View citations in EconPapers (2)

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