作者：Glasserman, Paul; Kou, Shing-Gang
作者单位：Columbia University; Columbia University
摘要：We consider limits of first passage times to indexed families of nested sets in regenerative processes. The sets are exponentially rare, in the sense that the probability that the process reaches an indexed set in a cycle vanishes exponentially fast in the indexing parameter. Under appropriate formulations of this hypothesis, we prove strong laws, iterated logarithm laws and limits in distribution, both for the index of the rarest set reached in a cycle and for the time to reach a set. An inte...
作者：Athreya, K. B.; Vidyashankar, A. N.
作者单位：Iowa State University
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 con...
