@book{43359a85242c47dd88c56405cd190434,

title = "Asymptotic period of an aperiodic Markov chain and the strong ratio limit property",

abstract = "We introduce the concept of asymptotic period for an irreducible and aperiodic discrete-time Markov chain on a countable state space. If the chain is transient its asymptotic period may be larger than one. We present some sufficient conditions and, in the more restricted setting of birth-death processes, a necessary and sufficient condition for asymptotic aperiodicity. It is subsequently shown that a birth-death process has the strong ratio limit property if a related birth-death process is asymptotically aperiodic. In the general setting a similar statement is not true, but validity of the converse implication is posed as a conjecture.",

keywords = "ratio limit, invariant vector, Invariant Measure, transition probability, transient Markov chain, period, IR-104041, aperiodicity, Birth-death process, MSC-60J10, EWI-27823, MSC-60J80, harmonic function",

author = "{van Doorn}, {Erik A.}",

year = "2017",

month = mar,

language = "Undefined",

series = "Memorandum / Department of Applied Mathematics",

publisher = "University of Twente",

number = "2059",

address = "Netherlands",

}