Regularity and approximability of the solutions to the chemical master equation

Ludwig Gauckler; Harry Yserentant

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique (2014)

  • Volume: 48, Issue: 6, page 1757-1775
  • ISSN: 0764-583X

Abstract

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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 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.

How to cite

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Gauckler, Ludwig, and Yserentant, Harry. "Regularity and approximability of the solutions to the chemical master equation." ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique 48.6 (2014): 1757-1775. <http://eudml.org/doc/273151>.

@article{Gauckler2014,
abstract = {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.},
author = {Gauckler, Ludwig, Yserentant, Harry},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique},
keywords = {chemical master equation; existence of solutions and moments; error of finite state projections},
language = {eng},
number = {6},
pages = {1757-1775},
publisher = {EDP-Sciences},
title = {Regularity and approximability of the solutions to the chemical master equation},
url = {http://eudml.org/doc/273151},
volume = {48},
year = {2014},
}

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 - Modélisation Mathématique et Analyse Numérique
PY - 2014
PB - EDP-Sciences
VL - 48
IS - 6
SP - 1757
EP - 1775
AB - 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.
LA - eng
KW - chemical master equation; existence of solutions and moments; error of finite state projections
UR - http://eudml.org/doc/273151
ER -

References

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