Solidarity and ergodic properties of semi-Markov transition probabilities
Date
1968
Authors
Cheong, Choong Kong
Journal Title
Journal ISSN
Volume Title
Publisher
Abstract
The chief purpose of this thesis is to establish for semi-Markov
processes the same type of behaviour that is characteristic of the
better-known Markov chains; this is achieved mainly through the use
of Laplace and Laplace-Stieltjes transforms and a frequent appeal to
renewal theory. The mathematical tools needed for the task are
developed in the first chapter. In the second chapter the solidarity
nature of geometric ergodicity within an irreducible class is
examined, and necessary and sufficient conditions are derived for
geometric ergodicity in the particular case of a process with a finite
state space. In chapter three it is shown that the Laplace transforms
of the transition probabilities pertaining to an irreducible class all
have the same abscissa of convergence, a fact that permits the definition
of a-recurrence and leads to a result for a-recurrent processes that
generalizes the familiar ergodic theorem of Markov chain theory;
quasi-stationary distributions are also studied in the same chapter.
Chapter four is devoted to some general ratio-limit theorems involving
a parameter λ (λ equals zero in the usual ratio-limit theorems),
and the last chapter applies the results obtained in the earlier part
of the thesis to the study of an inventory model and a continuous-time
Markov branching process.
Description
Keywords
Citation
Collections
Source
Type
Thesis (PhD)
Book Title
Entity type
Access Statement
License Rights
Restricted until
Downloads
File
Description