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@article{Thomas:2015:10.1103/PhysRevE.92.012120,
author = {Thomas, P and Grima, R},
doi = {10.1103/PhysRevE.92.012120},
journal = {Physical Review E},
pages = {012120--012120--12},
title = {Approximate probability distributions of the master equation},
url = {http://dx.doi.org/10.1103/PhysRevE.92.012120},
volume = {92},
year = {2015}
}

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TY  - JOUR
AB  - Master equations are common descriptions of mesoscopic systems. Analytical solutions to these equations can rarely be obtained. We here derive an analytical approximation of the time-dependent probability distribution of the master equation using orthogonal polynomials. The solution is given in two alternative formulations: a series with continuous and a series with discrete support, both of which can be systematically truncated. While both approximations satisfy the system size expansion of the master equation, the continuous distribution approximations become increasingly negative and tend to oscillations with increasing truncation order. In contrast, the discrete approximations rapidly converge to the underlying non-Gaussian distributions. The theory is shown to lead to particularly simple analytical expressions for the probability distributions of molecule numbers in metabolic reactions and gene expression systems.
AU  - Thomas,P
AU  - Grima,R
DO  - 10.1103/PhysRevE.92.012120
EP  - 012120
PY  - 2015///
SN  - 1539-3755
SP  - 012120
TI  - Approximate probability distributions of the master equation
T2  - Physical Review E
UR  - http://dx.doi.org/10.1103/PhysRevE.92.012120
UR  - http://hdl.handle.net/10044/1/38734
VL  - 92
ER  -

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