Strong stationary duality for continuous-time Markov chains. Part I: Theory

1992 ◽  
Vol 5 (1) ◽  
pp. 45-70 ◽  
Author(s):  
James Allen Fill
Keyword(s):  
Markov Chains ◽  
Continuous Time ◽  
Continuous Time Markov Chains ◽  
Strong Stationary Duality

scholarly journals Strong Stationary Duality and Algebraic Duality for Continuous Time Möbius Monotone Markov Chains

2021 ◽  
Vol 15 (2) ◽  
pp. 69-86
Author(s):  
Pan Zhao ◽  
Keyword(s):  
Markov Chains ◽  
State Space ◽  
Continuous Time ◽  
Two Dimensional ◽  
Partially Ordered ◽  
Continuous Time Markov Chains ◽  
Strong Stationary Duality ◽  
Birth And Death Chain ◽  
Algebraic Duality ◽  
Ordered State

Under the assumption of Möbius monotonicity, we develop the theory of strong stationary duality for continuous time Markov chains on the finite partially ordered state space, we also construct a nonexplosive algebraic duality for continuous time Markov chains on Finally, we present an application to the two-dimensional birth and death chain.

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.

Sign in / Sign up

Export Citation Format

Share Document