Abstract
Let {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.
Original language | English (US) |
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Pages (from-to) | 57-71 |
Number of pages | 15 |
Journal | Stochastic Processes and their Applications |
Volume | 50 |
Issue number | 1 |
DOIs | |
State | Published - 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