A modified uniformization method for the solution of the chemical master equation

DOI10.1016/j.camwa.2009.04.021zbMath1189.34087OpenAlexW2028916057MaRDI QIDQ980387

Layne T. Watson, Yang Cao, Jingwei Zhang

Publication date: 28 June 2010

Published in: Computers \& Mathematics with Applications (Search for Journal in Brave)

Full work available at URL: http://eprints.cs.vt.edu/archive/00000992/01/IETSB07.pdf

zbMATH Keywords

systems biologychemical master equationstochastic simulation algorithmexternal uniformization method

Mathematics Subject Classification ID

Classical flows, reactions, etc. in chemistry (92E20) Qualitative investigation and simulation of ordinary differential equation models (34C60) Genetics and epigenetics (92D10) Applications of continuous-time Markov processes on discrete state spaces (60J28)

Related Items (5)

Product Form Approximation of Transient Probabilities in Stochastic Reaction Networks ⋮ Approximation of event probabilities in noisy cellular processes ⋮ Hybrid discrete/continuum algorithms for stochastic reaction networks ⋮ Markovian dynamics on complex reaction networks ⋮ Approximate analysis of biological systems by hybrid switching jump diffusion

Uses Software

• Expokit
• UMFPACK
• ITSOL
• ARPACK
• SPARSKIT
• CSparse

Cites Work

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• Multiscale stochastic simulation algorithm with stochastic partial equilibrium assumption for chemically reacting systems
• Solving the chemical master equation for monomolecular reaction systems analytically
• A solver for the stochastic master equation applied to gene regulatory networks
• Numerical transient analysis of Markov models
• A numerical study of large sparse matrix exponentials arising in Markov chains.
• Deterministic parallel global parameter estimation for a model of the budding yeast cell cycle
• Approximating Transition Probabilities and Mean Occupation Times in Continuous-Time Markov Chains
• Bounds and Approximations for the Transient Behavior of Continuous-Time Markov Chains
• Direct Methods for Sparse Linear Systems
• Some Bounds on the Error in Approximating Transition Probabilities in Continuous-Time Markov Processes
• Expokit
• Nineteen Dubious Ways to Compute the Exponential of a Matrix, Twenty-Five Years Later

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