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Regularity and approximability of the solutions to the chemical master equation

Please always quote using this URN:urn:nbn:de:0296-matheon-12146
  • The chemical master equation is a fundamental equation in chemical kinetics. It is an adequate substitute for the classical reaction-rate equations whenever stochastic effects become relevant. In the present paper we give a simple argument showing that the solutions of a large class of chemical master equations, including all those in which elementary reactions between two and more molecules do not generate a larger number of molecules than existed before, are bounded in weighted $\ell_1$-spaces. 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 of the finite state projection of the chemical master equation, an approximation that underlies many numerical methods.

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Metadaten
Author:Ludwig Gauckler, Harry Yserentant
URN:urn:nbn:de:0296-matheon-12146
Referee:Peter Deuflhard
Document Type:Preprint, Research Center Matheon
Language:English
Date of first Publication:2013/05/09
Release Date:2013/05/09
Tag:chemical master equation; finite state projections; regularity
Institute: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:1010
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