Compactification of the discrete state space of a Markov process

1968 ◽  
Vol 10 (3) ◽  
pp. 236-251 ◽  
Author(s):  
J. L. Doob
Keyword(s):  
Markov Process ◽  
State Space ◽  
Discrete State ◽  
Discrete State Space

Randomization of intensities in a Markov chain

1979 ◽  
Vol 11 (2) ◽  
pp. 397-421 ◽  
Author(s):  
M. Yadin ◽  
R. Syski
Keyword(s):  
Markov Chain ◽  
Markov Process ◽  
State Space ◽  
Continuous Time ◽  
Markovian Process ◽  
Time Parameter ◽  
Discrete State ◽  
Intensity Matrix ◽  
The Matrix ◽  
Discrete State Space

The matrix of intensities of a Markov process with discrete state space and continuous time parameter undergoes random changes in time in such a way that it stays constant between random instants. The resulting non-Markovian process is analyzed with the help of supplementary process defined in terms of variations of the intensity matrix. Several examples are presented.

Randomization of intensities in a Markov chain

1979 ◽  
Vol 11 (02) ◽  
pp. 397-421
Author(s):  
M. Yadin ◽  
R. Syski
Keyword(s):  
Markov Chain ◽  
Markov Process ◽  
State Space ◽  
Continuous Time ◽  
Markovian Process ◽  
Time Parameter ◽  
Discrete State ◽  
Intensity Matrix ◽  
The Matrix ◽  
Discrete State Space

The matrix of intensities of a Markov process with discrete state space and continuous time parameter undergoes random changes in time in such a way that it stays constant between random instants. The resulting non-Markovian process is analyzed with the help of supplementary process defined in terms of variations of the intensity matrix. Several examples are presented.

scholarly journals Improved estimations of stochastic chemical kinetics by finite-state expansion

2021 ◽  
Vol 477 (2251) ◽  
pp. 20200964
Author(s):  
Tabea Waizmann ◽  
Luca Bortolussi ◽  
Andrea Vandin ◽  
Mirco Tribastone
Keyword(s):  
Master Equation ◽  
State Space ◽  
Stochastic Dynamics ◽  
Reaction Network ◽  
Discrete State ◽  
State Expansion ◽  
Analytical Approximations ◽  
Finite State ◽  
Stochastic Reaction ◽  
Discrete State Space

Stochastic reaction networks are a fundamental model to describe interactions between species where random fluctuations are relevant. The master equation provides the evolution of the probability distribution across the discrete state space consisting of vectors of population counts for each species. However, since its exact solution is often elusive, several analytical approximations have been proposed. The deterministic rate equation (DRE) gives a macroscopic approximation as a compact system of differential equations that estimate the average populations for each species, but it may be inaccurate in the case of nonlinear interaction dynamics. Here we propose finite-state expansion (FSE), an analytical method mediating between the microscopic and the macroscopic interpretations of a stochastic reaction network by coupling the master equation dynamics of a chosen subset of the discrete state space with the mean population dynamics of the DRE. An algorithm translates a network into an expanded one where each discrete state is represented as a further distinct species. This translation exactly preserves the stochastic dynamics, but the DRE of the expanded network can be interpreted as a correction to the original one. The effectiveness of FSE is demonstrated in models that challenge state-of-the-art techniques due to intrinsic noise, multi-scale populations and multi-stability.

A novel recursive T-S fuzzy semantic modeling approach for discrete state-space systems

2019 ◽  
Vol 340 ◽  
pp. 222-232 ◽  
Author(s):  
Liang-Qun Li ◽  
Xiao-Li Wang ◽  
Wei-Xin Xie ◽  
Zong-Xiang Liu
Keyword(s):  
State Space ◽  
Space Systems ◽  
Semantic Modeling ◽  
Discrete State ◽  
Modeling Approach ◽  
State Space Systems ◽  
Discrete State Space
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