Dynamics of the Chemical Master Equation, a strip of chains of equations in d-dimensional space

Abstract

We investigate the multi-chain version of the Chemical Master Equation, when there are transitions between different states inside the long chains, as well as transitions between (a few) different chains. In the discrete version, such a model can describe the connected diffusion processes with jumps between different types. We apply the Hamilton-Jacobi equation to solve some aspects of the model. We derive exact {(in the limit of infinite number of particles)} results for the dynamic of the maximum of the distribution and the variance of distribution.

9 pages

References in corpus (9)

• Extinction of metastable stochastic populations
• Determining the stability of genetic switches: explicitly accounting for mRNA noise
• Spectral solutions to stochastic models of gene expression with bursts and regulation
• Exactly solvable dynamics of the Eigen and the Crow-Kimura models
• Evolution Equation of Phenotype Distribution: General Formulation and Application to Error Catastrophe
• Exact solution of a two-type branching process: Clone size distribution in cell division kinetics
• Evolution models with base substitutions, insertions, deletions and selection
• Analytical study of an exclusive genetic switch
• Exact results in the large system size limit for the dynamics of the Chemical Master Equation, a one dimensional chain of equations

Cited by in corpus (4)

• Mathematical Formalism of Nonequilibrium Thermodynamics for Nonlinear Chemical Reaction Systems with General Rate Law
• The Hamilton-Jacobi Equation: an intuitive approach
• Exact probability distribution functions for Parrondo's games
• Statistical properties and error threshold of quasispecies on single-peak Gaussian-distributed fitness landscapes