scholarly journals Weak convergence of first-rare-event times for semi-Markov processes

2020 ◽  
Author(s):  
AISDL
Keyword(s):  
Weak Convergence ◽  
Markov Processes ◽  
Sufficient Conditions ◽  
Rare Event ◽  
Necessary And Sufficient Conditions ◽  
Finite Set ◽  
In Series ◽  
Event Times ◽  
Semi Markov Processes ◽  
Necessary And Sufficient

Necessary and sufficient conditions for weak convergence of first-rareevent times for semi-Markov processes with finite set of states in series of schemes are obtained.

On the weak convergence of sequences of circuit processes: a probabilistic approach

1992 ◽  
Vol 29 (02) ◽  
pp. 374-383 ◽  
Author(s):  
Sophia Kalpazidou
Keyword(s):  
Markov Chain ◽  
Weak Convergence ◽  
Asymptotic Behaviour ◽  
Markov Processes ◽  
Probabilistic Approach ◽  
Probabilistic Interpretation ◽  
Sample Paths ◽  
Convergence Of Sequences ◽  
Recurrent Markov Chain ◽  
Positive Recurrent

The asymptotic behaviour of sequences of Markov processes whose finite distributions depend upon the sample paths ω of a positive recurrent Markov chain ξ is studied. The existence of such sequences depends upon the existence of a unique class of directed weighted circuits having a probabilistic interpretation in terms of the directed circuits occurring along the sample paths of ξ. An application to multiple Markov chains is given.

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