Abstract/Details

ON SOME PROBLEMS IN THE THEORY OF NON-HOMOGENEOUS MARKOV CHAINS

CHATTOPADHYAY, RITA. 
 University of South Florida ProQuest Dissertations Publishing,  1984. 8427955.

Abstract (summary)

Some general and well-known definitions are properties of homogeneous Markov chains are first given. By extending these definitions to non-homogeneous Markov chains some general properties of the latter are derived. Most of the extensions deal with essential, inessential, recurrence and periodic properties of the state space of a non-homogeneous Markov chain. Whenever the non-homogeneous analogue of a well-known homogeneous chain property fails, a counterexample is usually given.

Next, Doeblin's theorem giving the ergodic behaviour of a certain class of non-homogeneous chains is given. Some well-known theorems on weak ergodicity are stated. Then Doeblin's condition is relaxed to give Doeblin-like results for a class of non-homogeneous chains which contain, as a subset, the class of chains satisfying Doeblin's condition. Some examples are discussed to justify the assumptions involved.

The final chapter considers an extension of some properties of the basis of a convergent non-homogeneous Markov chain from a finite state space to a countably infinite state space. Some known examples are discussed to explain the modifications in the latter case.

Indexing (details)


Subject
Mathematics
Classification
0405: Mathematics
Identifier / keyword
Pure sciences
Title
ON SOME PROBLEMS IN THE THEORY OF NON-HOMOGENEOUS MARKOV CHAINS
Author
CHATTOPADHYAY, RITA
Number of pages
69
Degree date
1984
School code
0206
Source
DAI-B 45/09, Dissertation Abstracts International
Place of publication
Ann Arbor
Country of publication
United States
ISBN
9798413196151
University/institution
University of South Florida
University location
United States -- Florida
Degree
Ph.D.
Source type
Dissertation or Thesis
Language
English
Document type
Dissertation/Thesis
Dissertation/thesis number
8427955
ProQuest document ID
303325443
Copyright
Database copyright ProQuest LLC; ProQuest does not claim copyright in the individual underlying works.
Document URL
https://www.proquest.com/docview/303325443