A numerical characteristic method for probability generating functions on stochastic first-order reaction networks
- Authors
- Lee, Chang Hyeong; Shin, Jaemin; Kim, Junseok
- Issue Date
- 1월-2013
- Publisher
- SPRINGER
- Keywords
- First-order reaction network; Characteristic method; Monte Carlo method; First-order partial differential equation
- Citation
- JOURNAL OF MATHEMATICAL CHEMISTRY, v.51, no.1, pp.316 - 337
- Indexed
- SCIE
SCOPUS
- Journal Title
- JOURNAL OF MATHEMATICAL CHEMISTRY
- Volume
- 51
- Number
- 1
- Start Page
- 316
- End Page
- 337
- URI
- https://scholar.korea.ac.kr/handle/2021.sw.korea/104258
- DOI
- 10.1007/s10910-012-0085-8
- ISSN
- 0259-9791
- 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.
- Files in This Item
- There are no files associated with this item.
- Appears in
Collections - College of Science > Department of Mathematics > 1. Journal Articles
Items in ScholarWorks are protected by copyright, with all rights reserved, unless otherwise indicated.