Large deviations for distributions of sums of random variables: Markov chain method |
| |
Authors: | V. R. Fatalov |
| |
Affiliation: | 1.Faculty of Mechanics and Mathematics,Lomonosov Moscow State University,Moscow,Russia |
| |
Abstract: | Let {ξ k } k=0∞ be a sequence of i.i.d. real-valued random variables, and let g(x) be a continuous positive function. Under rather general conditions, we prove results on sharp asymptotics of the probabilities $
Pleft{ {frac{1}
{n}sumlimits_{k = 0}^{n - 1} {gleft( {xi _k } right) < d} } right}
$
Pleft{ {frac{1}
{n}sumlimits_{k = 0}^{n - 1} {gleft( {xi _k } right) < d} } right}
, n → ∞, and also of their conditional versions. The results are obtained using a new method developed in the paper, namely, the Laplace method for sojourn times of discrete-time Markov chains. We consider two examples: standard Gaussian random variables with g(x) = |x| p , p > 0, and exponential random variables with g(x) = x for x ≥ 0. |
| |
Keywords: | |
本文献已被 SpringerLink 等数据库收录! |
|