Abstract
For a Markov chain with an arbitrary nonempty state space, with stationary finitely additive transition probabilities and with initial distribution concentrated on a recurrent state, it is shown that the probability of every tail set is either zero or one. This generalizes and in particular gives an alternative proof of the result due to Blackwell and Freedman [1] in case the state space is countable and all transition probabilities are countably additive.
| Original language | English (US) |
|---|---|
| Pages (from-to) | 493-497 |
| Number of pages | 5 |
| Journal | Proceedings of the American Mathematical Society |
| Volume | 89 |
| Issue number | 3 |
| DOIs | |
| State | Published - Jan 1 1983 |
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ASJC Scopus subject areas
- Mathematics(all)
- Applied Mathematics
Cite this
The tail σ-field of a finitely additive Markov chain starting from a recurrent state. / Ramakrishnan, Subramanian.
In: Proceedings of the American Mathematical Society, Vol. 89, No. 3, 01.01.1983, p. 493-497.Research output: Contribution to journal › Article
}
TY - JOUR
T1 - The tail σ-field of a finitely additive Markov chain starting from a recurrent state
AU - Ramakrishnan, Subramanian
PY - 1983/1/1
Y1 - 1983/1/1
N2 - For a Markov chain with an arbitrary nonempty state space, with stationary finitely additive transition probabilities and with initial distribution concentrated on a recurrent state, it is shown that the probability of every tail set is either zero or one. This generalizes and in particular gives an alternative proof of the result due to Blackwell and Freedman [1] in case the state space is countable and all transition probabilities are countably additive.
AB - For a Markov chain with an arbitrary nonempty state space, with stationary finitely additive transition probabilities and with initial distribution concentrated on a recurrent state, it is shown that the probability of every tail set is either zero or one. This generalizes and in particular gives an alternative proof of the result due to Blackwell and Freedman [1] in case the state space is countable and all transition probabilities are countably additive.
UR - http://www.scopus.com/inward/record.url?scp=84966198413&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=84966198413&partnerID=8YFLogxK
U2 - 10.1090/S0002-9939-1983-0715873-2
DO - 10.1090/S0002-9939-1983-0715873-2
M3 - Article
AN - SCOPUS:84966198413
VL - 89
SP - 493
EP - 497
JO - Proceedings of the American Mathematical Society
JF - Proceedings of the American Mathematical Society
SN - 0002-9939
IS - 3
ER -