THE RUIN PROBLEM FOR FINITE MARKOV-CHAINS
成果类型：
Article
署名作者：
HOGLUND, T
刊物名称：
ANNALS OF PROBABILITY
ISSN/ISSBN：
0091-1798
DOI：
10.1214/aop/1176990345
发表日期：
1991
页码：
1298-1310
关键词：
摘要：
We derive an asymptotic approximation of the joint distribution prob(N(u) - n is-an-element-of A, S(N(u)) - u is-element-of B) as n and u --> infinity. Here N(u) = min{n; S(n) > u} denotes the first passage time for a random walk of the form S(n) = SIGMA-k = 1n U(k)(xi-k - 1, xi-k), where xi-0, xi-1,... is a finite Markov chain and where {U(k)(i, j)} infinity(k = 1) is a sequence of independent random variables. The approximation holds for all sets B and a fairly large class of sets A.