Limit theorems for semi-Markov processes and renewal theory for Markov chains on general state spaces

1978 ◽  
Vol 10 (2) ◽  
pp. 292-293 ◽  
Author(s):  
K. B. Athreya ◽  
P. Ney
Keyword(s):  
Markov Chains ◽  
Markov Processes ◽  
Limit Theorems ◽  
Renewal Theory ◽  
General State ◽  
State Spaces ◽  
Semi Markov Processes

scholarly journals Limit theorems for semi-Markov processes

1978 ◽  
Vol 19 (2) ◽  
pp. 283-294 ◽  
Author(s):  
K.B. Athreya ◽  
P.E. Ney
Keyword(s):  
Markov Processes ◽  
Limit Theorems ◽  
General State ◽  
State Spaces ◽  
New Construction ◽  
Regeneration Times ◽  
Semi Markov Processes

A new construction of regeneration times is exploited to prove ergodic and renewal theorems for semi-Markov processes on general state spaces. This work extends results of the authors in Ann. Probability (6 (1978), 788–797).

Geometrical aspects of the theory of non-homogeneous Markov chains

1975 ◽  
Vol 77 (1) ◽  
pp. 171-183 ◽  
Author(s):  
J. F. C. Kingman
Keyword(s):  
Markov Chains ◽  
Markov Processes ◽  
Convex Sets ◽  
Projective Limit ◽  
Embedding Problem ◽  
General State ◽  
Transition Matrices ◽  
State Spaces ◽  
Geometrical Representation ◽  
Simple Corollary

AbstractA geometrical representation of the transition matrices of a non-homogeneous chain with N states, in terms of certain convex subsets of , is used to describe aspects of the chain. For example, an important theorem of Cohn on the structure of the tail σ-field is a simple corollary. The embedding problem is shown to be entirely geometrical in character. The representation extends to Markov processes on quite general state spaces, and the tail is then represented by the projective limit of these convex sets.

Semi-Markov processes on a general state space: α-theory and quasi-stationarity

1980 ◽  
Vol 30 (2) ◽  
pp. 187-200 ◽  
Author(s):  
E. Arjas ◽  
E. Nummelin ◽  
R. L. Tweedie
Keyword(s):  
State Space ◽  
Markov Processes ◽  
Limit Theorems ◽  
General State ◽  
General State Space ◽  
Quasistationary Distributions ◽  
Positive Recurrent ◽  
Semi Markov Processes

AbstractBy amalgamating the approaches of Tweedie (1974) and Nummelin (1977), an α-theory is developed for general semi-Markov processes. It is shown that α-transient, α-recurrent and α-positive recurrent processes can be defined, with properties analogous to those for transient, recurrent and positive recurrent processes. Limit theorems for α-positive recurrent processes follow by transforming to the probabilistic case, as in the above references: these then give results on the existence and form of quasistationary distributions, extending those of Tweedie (1975) and Nummelin (1976).

MARKOV Processes in General State Spaces

1978 ◽  
Vol 86 (1) ◽  
pp. 67-83 ◽  
Author(s):  
H. J. Engelbert
Keyword(s):  
Markov Processes ◽  
General State ◽  
State Spaces
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