Abstract
In this paper we develop the theory of Markov chains with stationary transition probabilities, where the transition probabilities and the initial distribution are assumed only to be finitely additive. We prove a strong law of large numbers for recurrent chains. The problem of existence and uniqueness of finitely additive stationary initial distributions is studied and the ergodicity of recurrent chains under a stationary initial distribution is proved.
| Original language | English (US) |
|---|---|
| Pages (from-to) | 247-272 |
| Number of pages | 26 |
| Journal | Transactions of the American Mathematical Society |
| Volume | 265 |
| Issue number | 1 |
| DOIs | |
| State | Published - Jan 1 1981 |
| Externally published | Yes |
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Keywords
- Finitely additive probabilities
- Markov chain
- Markov strategy
- Stationary initial distribution
- Stationary transition
- Strategy
ASJC Scopus subject areas
- Mathematics(all)
- Applied Mathematics
Cite this
Finitely additive markov chains. / Ramakrishnan, Subramanian.
In: Transactions of the American Mathematical Society, Vol. 265, No. 1, 01.01.1981, p. 247-272.Research output: Contribution to journal › Article
}
TY - JOUR
T1 - Finitely additive markov chains
AU - Ramakrishnan, Subramanian
PY - 1981/1/1
Y1 - 1981/1/1
N2 - In this paper we develop the theory of Markov chains with stationary transition probabilities, where the transition probabilities and the initial distribution are assumed only to be finitely additive. We prove a strong law of large numbers for recurrent chains. The problem of existence and uniqueness of finitely additive stationary initial distributions is studied and the ergodicity of recurrent chains under a stationary initial distribution is proved.
AB - In this paper we develop the theory of Markov chains with stationary transition probabilities, where the transition probabilities and the initial distribution are assumed only to be finitely additive. We prove a strong law of large numbers for recurrent chains. The problem of existence and uniqueness of finitely additive stationary initial distributions is studied and the ergodicity of recurrent chains under a stationary initial distribution is proved.
KW - Finitely additive probabilities
KW - Markov chain
KW - Markov strategy
KW - Stationary initial distribution
KW - Stationary transition
KW - Strategy
UR - http://www.scopus.com/inward/record.url?scp=84968464910&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=84968464910&partnerID=8YFLogxK
U2 - 10.1090/S0002-9947-1981-0607119-3
DO - 10.1090/S0002-9947-1981-0607119-3
M3 - Article
AN - SCOPUS:84968464910
VL - 265
SP - 247
EP - 272
JO - Transactions of the American Mathematical Society
JF - Transactions of the American Mathematical Society
SN - 0002-9947
IS - 1
ER -