Regularity and approximability of the solutions to the chemical master equation

Please always quote using this URN:urn:nbn:de:0296-matheon-12781

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 $\ell_1$-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.

Metadaten
Author:	Ludwig Gauckler, Harry Yserentant
URN:	urn:nbn:de:0296-matheon-12781
Referee:	Benjamin Kunz
Document Type:	Preprint, Research Center Matheon
Language:	English
Date of first Publication:	2016/01/21
Release Date:	2016/01/21
Tag:	chemical master equation; error of finite state projections; existence of solutions and moments
Institute:	Research Center Matheon
	Technische Universität Berlin
MSC-Classification:	60-XX PROBABILITY THEORY AND STOCHASTIC PROCESSES (For additional applications, see 11Kxx, 62-XX, 90-XX, 91-XX, 92-XX, 93-XX, 94-XX) / 60Jxx Markov processes / 60J27 Continuous-time Markov processes on discrete state spaces
	65-XX NUMERICAL ANALYSIS / 65Lxx Ordinary differential equations / 65L05 Initial value problems
	65-XX NUMERICAL ANALYSIS / 65Lxx Ordinary differential equations / 65L70 Error bounds
	80-XX CLASSICAL THERMODYNAMICS, HEAT TRANSFER (For thermodynamics of solids, see 74A15) / 80Axx Thermodynamics and heat transfer / 80A30 Chemical kinetics [See also 76V05, 92C45, 92E20]
Preprint Number:	1096

Open Access