The chemical master equation is a fundamental equation in chemical kinetics. It underlies the classical reaction-rate equations and takes stochastic effects into account. In this paper we give a simple argument showing that the solutions of a large class of chemical master equations are bounded in weighted ℓ1-spaces and possess high-order moments. This class includes all equations in which no reactions between two or more already present molecules and further external reactants occur that add mass to the system. As an illustration for the implications of this kind of regularity, we analyze the effect of truncating the state space. This leads to an error analysis for the finite state projections of the chemical master equation, an approximation that forms the basis of many numerical methods.
Mots-clés : chemical master equation, existence of solutions and moments, error of finite state projections
@article{M2AN_2014__48_6_1757_0,
author = {Gauckler, Ludwig and Yserentant, Harry},
title = {Regularity and approximability of the solutions to the chemical master equation},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis },
pages = {1757--1775},
publisher = {EDP-Sciences},
volume = {48},
number = {6},
year = {2014},
doi = {10.1051/m2an/2014018},
language = {en},
url = {http://www.numdam.org/articles/10.1051/m2an/2014018/}
}
TY - JOUR AU - Gauckler, Ludwig AU - Yserentant, Harry TI - Regularity and approximability of the solutions to the chemical master equation JO - ESAIM: Mathematical Modelling and Numerical Analysis PY - 2014 SP - 1757 EP - 1775 VL - 48 IS - 6 PB - EDP-Sciences UR - http://www.numdam.org/articles/10.1051/m2an/2014018/ DO - 10.1051/m2an/2014018 LA - en ID - M2AN_2014__48_6_1757_0 ER -
%0 Journal Article %A Gauckler, Ludwig %A Yserentant, Harry %T Regularity and approximability of the solutions to the chemical master equation %J ESAIM: Mathematical Modelling and Numerical Analysis %D 2014 %P 1757-1775 %V 48 %N 6 %I EDP-Sciences %U http://www.numdam.org/articles/10.1051/m2an/2014018/ %R 10.1051/m2an/2014018 %G en %F M2AN_2014__48_6_1757_0
Gauckler, Ludwig; Yserentant, Harry. Regularity and approximability of the solutions to the chemical master equation. ESAIM: Mathematical Modelling and Numerical Analysis , Tome 48 (2014) no. 6, pp. 1757-1775. doi : 10.1051/m2an/2014018. http://www.numdam.org/articles/10.1051/m2an/2014018/
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