Regularity and approximability of the solutions to the chemical master equation
ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique, Volume 48 (2014) no. 6, p. 1757-1775
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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 1-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.

DOI : https://doi.org/10.1051/m2an/2014018
Classification:  80A30,  60J27,  65L05,  65L70
Keywords: 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 - Mod\'elisation Math\'ematique et Analyse Num\'erique},
     publisher = {EDP-Sciences},
     volume = {48},
     number = {6},
     year = {2014},
     pages = {1757-1775},
     doi = {10.1051/m2an/2014018},
     language = {en},
     url = {http://www.numdam.org/item/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 - Modélisation Mathématique et Analyse Numérique, Volume 48 (2014) no. 6, pp. 1757-1775. doi : 10.1051/m2an/2014018. http://www.numdam.org/item/M2AN_2014__48_6_1757_0/

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