Markov additive processes and Perron-Frobenius eigenvalue inequalities
成果类型：
Article
署名作者：
O'Cinneide, C
署名单位：
Purdue University System; Purdue University
刊物名称：
ANNALS OF PROBABILITY
ISSN/ISSBN：
0091-1798
DOI：
10.1214/aop/1019160333
发表日期：
2000
页码：
1230-1258
关键词：
摘要：
We present a method for proving Perron-Frobenius eigenvalue inequalities. The method is to apply Jensen's inequality to the change in a random evolution over a regenerative cycle of the underlying finite-state Markov chain. One of the primary benefits of the method is that it readily gives necessary and sufficient conditions for strict inequality. It also gives insights into some of the conjectures of J. E. Cohen. Ney and Nummelin's Hypothesis 2 arises here as a condition for strict inequality, and we explore its ramifications in detail for a special family of Markov additive processes which we call fluid models. This leads to a connection between Hypothesis 2 and the condition P-T P irreducible which arose in the work of Cohen, Friedland, Kato and Kelly.
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