ON THE PROBLEMS OF INHOMOGENOUS DISCRETE OUTPUT
成果类型：
Article
署名作者：
Miclo, Laurent
署名单位：
Universite de Toulouse; Universite Toulouse III - Paul Sabatier; Centre National de la Recherche Scientifique (CNRS)
刊物名称：
ANNALS OF APPLIED PROBABILITY
ISSN/ISSBN：
1050-5164
发表日期：
1996
页码：
1112-1156
关键词：
摘要：
Let (X-(t))(t >= 0) be a family of inhomogeneous Markov processes on a fi nite set M, whose jump intensities at the time s >= 0 are given by exp (-beta((t))(s) V(x, y))q(x, y) for all x not equal y epsilon M, where the evolutions of the inverse of the temperature R-1 Sic s bar right arrow beta((t))(s) epsilon R-1 take in some ways greater and greater values with t. We study by using semigroup techniques the asymptotic behavior of the couple consisting of the renormalized exit time and exit position from sets which are a little more general than the cycles associated with the cost function V. We obtain a general criterion for weak convergence, for which we describe explicitly the limit law. Then we are interested in the particular case of evolution families satisfying for all t, s >= 0, beta((t))(s) = beta((0))(t+s,) for which we show there are only three kinds of limit laws for the renormalized exit time (this is relevant for the limit theorems satisfied by renormalized occupation times of generalized simulated annealing algorithms, but this point will not be developed here).