A numerical characteristic method for probability generating functions on stochastic first-order reaction networks

Chang Hyeong Lee, Jaemin Shin, Junseok Kim

Research output: Contribution to journalArticle

1 Citation (Scopus)

Abstract

We propose an efficient and accurate numerical scheme for solving probability generating functions arising in stochastic models of general first-order reaction networks by using the characteristic curves. A partial differential equation derived by a probability generating function is the transport equation with variable coefficients. We apply the idea of characteristics for the estimation of statistical measures, consisting of the mean, variance, and marginal probability. Estimation accuracy is obtained by the Newton formulas for the finite difference and time accuracy is obtained by applying the fourth order Runge-Kutta scheme for the characteristic curve and the Simpson method for the integration on the curve. We apply our proposed method to motivating biological examples and show the accuracy by comparing simulation results from the characteristic method with those from the stochastic simulation algorithm.

Original languageEnglish
Pages (from-to)316-337
Number of pages22
JournalJournal of Mathematical Chemistry
Volume51
Issue number1
DOIs
Publication statusPublished - 2013 Jan 1

Fingerprint

Characteristics Method
Reaction Network
Probability generating function
Characteristic Curve
Numerical Methods
First-order
Runge-Kutta Schemes
Stochastic Simulation
Stochastic models
Variable Coefficients
Transport Equation
Numerical Scheme
Partial differential equations
Stochastic Model
Fourth Order
Finite Difference
Partial differential equation
Curve
Simulation

Keywords

  • Characteristic method
  • First-order partial differential equation
  • First-order reaction network
  • Monte Carlo method

ASJC Scopus subject areas

  • Chemistry(all)
  • Applied Mathematics

Cite this

A numerical characteristic method for probability generating functions on stochastic first-order reaction networks. / Lee, Chang Hyeong; Shin, Jaemin; Kim, Junseok.

In: Journal of Mathematical Chemistry, Vol. 51, No. 1, 01.01.2013, p. 316-337.

Research output: Contribution to journalArticle

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