Column continuous transition functions

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:328

Article

Li, Yangrong

关键词: continuous-time Markov chains;    transition functions;    q-matrices;    integrated semigroups;    generators;   

DOI  :  10.1016/j.jmaa.2006.05.001

来源: Elsevier

【 摘 要 】

A column continuous transition function is by definition a standard transition function P(t) whose every column is continuous for t >= 0 in the norm topology of bounded sequence space l(infinity). We will prove that it has a stable q-matrix and that there exists a one-to-one relationship between column continuous transition functions and increasing integrated semigroups on l(infinity). Using the theory of integrated semigroups, we give some necessary and sufficient conditions under which the minimal q-function is column continuous, in terms of its generator (of the Markov semigroup) as well as its q-matrix. Furthermore, we will construct all column continuous Q-functions for a conservative, single-exit and column bounded q-matrix Q. As applications, we find that many interesting continuous-time Markov chains (CTMCs), say Feller-Reuter-Riley processes, monotone processes, birth-death processes and branching processes, etc., have column continuity. (c) 2006 Elsevier Inc. All rights reserved.

【 授权许可】

Free