LARGE DEVIATION RATES FOR BRANCHING PROCESSES. II. THE MULTITYPE CASE
成果类型：
Article
署名作者：
Athreya, K. B.; Vidyashankar, A. N.
署名单位：
Iowa State University
刊物名称：
ANNALS OF APPLIED PROBABILITY
ISSN/ISSBN：
1050-5164
DOI：
10.1214/aoap/1177004778
发表日期：
1995
页码：
566-576
关键词：
摘要：
Let {Z(n) : n >= 0} be a p-type(p >= 2) supercritical branching process with mean matrix M. It is known that for any l in R-P, (l . Z(n)/1 . Z(n) - l . Z(n)M/1 . Z(n)) and (l . Z(n)/1 . Z(n) - l . upsilon((1))/1 . upsilon((1))) converge to 0 with probability 1 on the set of nonextinction, where upsilon((1)) is the left eigenvector of M corresponding to its maximal eigenvalue rho and 1 is the vector with all components equal to one. In this paper we study the large deviation aspects of this convergence. It is shown that the large deviation probabilities for these two sequences decay geometrically and under appropriate conditioning supergeometrically.