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On a paper by Doeblin on non-homogeneous Markov chains
- Source :
- Advances in Applied Probability. 13:388-401
- Publication Year :
- 1981
- Publisher :
- Cambridge University Press (CUP), 1981.
-
Abstract
- In [5] Doeblin considered some classes of finite non-homogeneous Markov chains and gave without proofs several results concerning their asymptotic behaviour. In the present paper we first attempt to make Doeblin's results precise and try to reconstruct his arguments. Subsequently we investigate more general situations, where a state space decomposition is provided by the sets occurring in the representation of the atomic sets of the tail or-field. We show that Doeblin's notion of an associated chain, as well as considerations regarding the tail ar-field structure of the chain, can be used to solve such cases. FINITE MARKOV CHAIN; FINAL CLASS; CYCLICALLY MOVING SUBCLASS; TAIL ar-FIELD; ATOMIC SET; RECURRENCE; WHIRLPOOL
- Subjects :
- Statistics and Probability
Pure mathematics
Class (set theory)
Markov chain
Applied Mathematics
010102 general mathematics
Structure (category theory)
Mathematical proof
01 natural sciences
Set (abstract data type)
010104 statistics & probability
Chain (algebraic topology)
Examples of Markov chains
0101 mathematics
Representation (mathematics)
Mathematics
Subjects
Details
- ISSN :
- 14756064 and 00018678
- Volume :
- 13
- Database :
- OpenAIRE
- Journal :
- Advances in Applied Probability
- Accession number :
- edsair.doi.dedup.....18255a157354d5c0967d496b8b066fb3