scholarly journals Random time-changes and asymptotic results for a class of continuous-time Markov chains on integers with alternating rates

2020 ◽  
pp. 1-29
Author(s):  
Luisa Beghin ◽  
Claudio Macci ◽  
Barbara Martinucci
Keyword(s):  
Markov Chains ◽  
Continuous Time ◽  
Random Time ◽  
Asymptotic Results ◽  
Continuous Time Markov Chains ◽  
Time Changes

Approximating Transition Probabilities and Mean Occupation Times in Continuous-Time Markov Chains

1987 ◽  
Vol 1 (3) ◽  
pp. 251-264 ◽  
Author(s):  
Sheldon M. Ross
Keyword(s):  
Markov Chains ◽  
Continuous Time ◽  
Transition Probabilities ◽  
Random Time ◽  
Occupation Times ◽  
New Approach ◽  
Continuous Time Markov Chains ◽  
The Mean ◽  
Mean Time

In this paper we propose a new approach for estimating the transition probabilities and mean occupation times of continuous-time Markov chains. Our approach is to approximate the probability of being in a state (or the mean time already spent in a state) at time t by the probability of being in that state (or the mean time already spent in that state) at a random time that is gamma distributed with mean t.

scholarly journals Subgeometric Ergodicity Analysis of Continuous-Time Markov Chains under Random-Time State-Dependent Lyapunov Drift Conditions

2014 ◽  
Vol 2014 ◽  
pp. 1-5
Author(s):  
Mokaedi V. Lekgari
Keyword(s):  
Markov Chains ◽  
Discrete Time ◽  
Continuous Time ◽  
Random Time ◽  
Lyapunov Analysis ◽  
Continuous Time Markov Chains ◽  
State Dependent ◽  
Drift Conditions

We investigate random-time state-dependent Foster-Lyapunov analysis on subgeometric rate ergodicity of continuous-time Markov chains (CTMCs). We are mainly concerned with making use of the available results on deterministic state-dependent drift conditions for CTMCs and on random-time state-dependent drift conditions for discrete-time Markov chains and transferring them to CTMCs.

scholarly journals Trace Machines for Observing Continuous-Time Markov Chains

2006 ◽  
Vol 153 (2) ◽  
pp. 259-277 ◽  
Author(s):  
Verena Wolf ◽  
Christel Baier ◽  
Mila Majster-Cederbaum
Keyword(s):  
Markov Chains ◽  
Continuous Time ◽  
Continuous Time Markov Chains

Bounds and Approximations for the Transient Behavior of Continuous-Time Markov Chains

1989 ◽  
Vol 3 (2) ◽  
pp. 175-198 ◽  
Author(s):  
Bok Sik Yoon ◽  
J. George Shanthikumar
Keyword(s):  
Markov Chains ◽  
Continuous Time ◽  
First Passage Time ◽  
Transient Behavior ◽  
Passage Time ◽  
Lower And Upper Bounds ◽  
Simple Method ◽  
Continuous Time Markov Chains ◽  
Recent Addition ◽  
Dependent Probability

Discretization is a simple, yet powerful tool in obtaining time-dependent probability distribution of continuous-time Markov chains. One of the most commonly used approaches is uniformization. A recent addition to such approaches is an external uniformization technique. In this paper, we briefly review these different approaches, propose some new approaches, and discuss their performances based on theoretical bounds and empirical computational results. A simple method to get lower and upper bounds for first passage time distribution is also proposed.

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