Exact Variance-Reduced Simulation of Lattice Continuous-Time Markov Chains with Applications in Reaction Networks

2019 ◽  
Vol 81 (8) ◽  
pp. 3159-3184 ◽  
Author(s):  
P. A. Maginnis ◽  
M. West ◽  
G. E. Dullerud
Keyword(s):  
Markov Chains ◽  
Continuous Time ◽  
Reaction Networks ◽  
Continuous Time Markov Chains

scholarly journals FORMALISMS FOR SPECIFYING MARKOVIAN POPULATION MODELS

2011 ◽  
Vol 22 (04) ◽  
pp. 823-841 ◽  
Author(s):  
THOMAS HENZINGER ◽  
BARBARA JOBSTMANN ◽  
VERENA WOLF
Keyword(s):  
Stochastic Process ◽  
Markov Chains ◽  
Continuous Time ◽  
Population Models ◽  
Ease Of Use ◽  
Stochastic Petri Nets ◽  
Reaction Networks ◽  
Process Algebras ◽  
Continuous Time Markov Chains ◽  
Stochastic Process Algebras

In this survey, we compare several languages for specifying Markovian population models such as queuing networks and chemical reaction networks. All these languages — matrix descriptions, stochastic Petri nets, stoichiometric equations, stochastic process algebras, and guarded command models — describe continuous-time Markov chains, but they differ according to important properties, such as compositionality, expressiveness and succinctness, executability, and ease of use. Moreover, they provide different support for checking the well-formedness of a model and for analyzing a model.

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.

scholarly journals Level 2.5 Large Deviations for Continuous-Time Markov Chains with Time Periodic Rates

2018 ◽  
Vol 19 (10) ◽  
pp. 3197-3238 ◽  
Author(s):  
Lorenzo Bertini ◽  
Raphael Chetrite ◽  
Alessandra Faggionato ◽  
Davide Gabrielli
Keyword(s):  
Markov Chains ◽  
Large Deviations ◽  
Continuous Time ◽  
Continuous Time Markov Chains ◽  
Time Periodic
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