Strong Ratio Limit Property for R-Recurrent Markov Chains

1965 ◽  
Vol 16 (2) ◽  
pp. 196 ◽  
Author(s):  
William E. Pruitt
Keyword(s):  
Markov Chains ◽  
Limit Property ◽  
Ratio Limit

scholarly journals Strong ratio limit property for $R$-recurrent Markov chains

1965 ◽  
Vol 16 (2) ◽  
pp. 196-196
Author(s):  
William E. Pruitt
Keyword(s):  
Markov Chains ◽  
Limit Property ◽  
Ratio Limit

scholarly journals The Strong Ratio Limit Property for Some General Markov Processes

1969 ◽  
Vol 40 (3) ◽  
pp. 986-992 ◽  
Author(s):  
Naresh C. Jain
Keyword(s):  
Markov Processes ◽  
Limit Property ◽  
Ratio Limit

A ratio limit theorem for (sub) Markov chains on {1,2, …} with bounded jumps

1995 ◽  
Vol 27 (3) ◽  
pp. 652-691 ◽  
Author(s):  
Harry Kesten
Keyword(s):  
Harmonic Function ◽  
Invariant Measure ◽  
Probability Measure ◽  
Markov Chains ◽  
Positive Matrices ◽  
Ratio Limit Theorems ◽  
Ratio Limit ◽  
A Chain ◽  
Image Position ◽  
Quasi Stationary Distribution

We consider positive matrices Q, indexed by {1,2, …}. Assume that there exists a constant 1 L < ∞ and sequences u1< u2< · ·· and d1d2< · ·· such that Q(i, j) = 0 whenever i < ur < ur + L < j or i > dr + L > dr > j for some r. If Q satisfies some additional uniform irreducibility and aperiodicity assumptions, then for s > 0, Q has at most one positive s-harmonic function and at most one s-invariant measure µ. We use this result to show that if Q is also substochastic, then it has the strong ratio limit property, that is for a suitable R and some R–1-harmonic function f and R–1-invariant measure µ. Under additional conditions µ can be taken as a probability measure on {1,2, …} and exists. An example shows that this limit may fail to exist if Q does not satisfy the restrictions imposed above, even though Q may have a minimal normalized quasi-stationary distribution (i.e. a probability measure µ for which R–1µ = µQ).The results have an immediate interpretation for Markov chains on {0,1,2, …} with 0 as an absorbing state. They give ratio limit theorems for such a chain, conditioned on not yet being absorbed at 0 by time n.

scholarly journals Strong ratio limit property

1961 ◽  
Vol 67 (6) ◽  
pp. 571-575 ◽  
Author(s):  
Steven Orey
Keyword(s):  
Limit Property ◽  
Ratio Limit

scholarly journals Strong Ratio Limit Theorems for $\phi$-Recurrent Markov Chains

1979 ◽  
Vol 7 (4) ◽  
pp. 639-650 ◽  
Author(s):  
E. Nummelin
Keyword(s):  
Markov Chains ◽  
Limit Theorems ◽  
Ratio Limit Theorems ◽  
Ratio Limit

scholarly journals Ratio limit theorems for Markov chains

1965 ◽  
Vol 15 (3) ◽  
pp. 989-1017 ◽  
Author(s):  
Sidney Port
Keyword(s):  
Markov Chains ◽  
Limit Theorems ◽  
Ratio Limit Theorems ◽  
Ratio Limit

scholarly journals Ratio limit theorems for Markov chains

1964 ◽  
Vol 15 (6) ◽  
pp. 907-907 ◽  
Author(s):  
J. F. C. Kingman ◽  
Steven Orey
Keyword(s):  
Markov Chains ◽  
Limit Theorems ◽  
Ratio Limit Theorems ◽  
Ratio Limit
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