R-POSITIVITY, QUASI-STATIONARY DISTRIBUTIONS AND RATIO LIMIT THEOREMS FOR A CLASS OF PROBABILISTIC AUTOMATA
成果类型：
Article
署名作者：
Ferrari, P. A.; Kesten, H.; Martinez, S.
署名单位：
Universidade de Sao Paulo; Cornell University; Universidad de Chile
刊物名称：
ANNALS OF APPLIED PROBABILITY
ISSN/ISSBN：
1050-5164
发表日期：
1996
页码：
577-616
关键词：
摘要：
We prove that certain (discrete time) probabilistic automata which can be absorbed in a null state have a normalized quasi-stationary distribution (when restricted to the states other than the null state). We also show that the conditional distribution of these systems, given that they are not absorbed before time n, converges to an honest probability distribution; this limit distribution is concentrated on the configurations with only finitely many active or occupied sites. A simple example to which our results apply is the discrete time version of the subcritical contact process on Z(d) or oriented percolation on Zd (for any d >= 1) as seen from the leftmost particle. For this and some related models we prove in addition a central limit theorem for n(-1/2) times the position of the leftmost particle (conditioned on survival until time n). The basic tool is to prove that our systems are R-positive-recurrent.