Large deviations for renewal processes

AbstractLet {Xn, n ⩾1} be a sequence of identically distributed real random variables with EX1 = μ > 0. Define Sn=Σni=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