LARGE DEVIATIONS FOR A RANDOM-WALK IN RANDOM ENVIRONMENT
成果类型：
Article
署名作者：
GREVEN, A; DENHOLLANDER, F
署名单位：
Radboud University Nijmegen
刊物名称：
ANNALS OF PROBABILITY
ISSN/ISSBN：
0091-1798
DOI：
10.1214/aop/1176988607
发表日期：
1994
页码：
1381-1428
关键词：
摘要：
Let omega = (p(x))(x epsilon Z) be an i.i.d, collection of (0, 1) valued random variables. Given omega, let (X(n))(n greater than or equal to 0) be the Markov chain on Z defined by X(0) = 0 and X(n+1) = X(n)+1(resp.X(n)-1) with probability p(Xn) (resp. 1-p(Xn)). It is shown that X(n)/n satisfies a large deviation principle with a continuous rate function, that is, [GRAPHICS] First, we derive a representation of the rate function I in terms of a variational problem. Second, we solve the latter explicitly in terms of random continued fractions. This leads to a classification and qualitative description of the shape of I. In the recurrent case I is nonanalytic at theta = 0. In the transient case I is nonanalytic at theta = -theta(c), 0, theta(c) for some theta(c) greater than or equal to 0, with linear pieces in between.