scholarly journals Limit Theorems for Semi-Markov Processes and Renewal Theory for Markov Chains

1978 ◽  
Vol 6 (5) ◽  
pp. 788-797 ◽  
Author(s):  
K. B. Athreya ◽  
D. McDonald ◽  
P. Ney
Keyword(s):  
Markov Chains ◽  
Markov Processes ◽  
Limit Theorems ◽  
Renewal Theory ◽  
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).

Limit theorems for α-recurrent semi-Markov processes

1976 ◽  
Vol 8 (03) ◽  
pp. 531-547 ◽  
Author(s):  
Esa Nummelin
Keyword(s):  
Markov Processes ◽  
Continuous Time ◽  
Limit Theorems ◽  
Transition Probabilities ◽  
Renewal Processes ◽  
Markov Renewal Processes ◽  
Semi Markov Process ◽  
Limit Behaviour ◽  
Semi Markov Processes ◽  
Special Case

In this paper the limit behaviour of α-recurrent Markov renewal processes and semi-Markov processes is studied by using the recent results on the concept of α-recurrence for Markov renewal processes. Section 1 contains the preliminary results, which are needed later in the paper. In Section 2 we consider the limit behaviour of the transition probabilities Pij (t) of an α-recurrent semi-Markov process. Section 4 deals with quasi-stationarity. Our results extend the results of Cheong (1968), (1970) and of Flaspohler and Holmes (1972) to the case in which the functions to be considered are directly Riemann integrable. We also try to correct the errors we have found in these papers. As a special case from our results we consider continuous-time Markov processes in Sections 3 and 5.

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