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

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.

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