@inbook{1393984d04284d2ca57358fd1c3ab9ab,

title = "On the regularity property of Semi-Markov processes with Borel state spaces",

abstract = "This note shows that a semi-Markov process with Borel state space is regular under a fairly weak condition on the mean sojourn or holding times and assuming that the embedded Markov chain satisfies one of the following conditions: (a) it is Harris recurrent; (b) it is recurrent and the “recurrent part” of the state space is reached with probability one for every initial state; (c) it has a unique invariant probability measure. Under the latter condition, the regularity property is only ensured for almost all initial states with respect to the invariant probability measure.",

keywords = "Borel Space, Embed Markov Chain, Invariant Probability Measure, Markov Chain, Regularity Property",

author = "{\'O}scar Vega-Amaya",

year = "2012",

month = jan,

day = "1",

doi = "10.1007/978-0-8176-8337-5_18",

language = "Ingl{\'e}s",

series = "Systems and Control: Foundations and Applications",

publisher = "Birkhauser Verlag Basel",

number = "9780817683368",

pages = "301--309",

booktitle = "Systems and Control",

address = "Suiza",

edition = "9780817683368",

}