The DOI matches its Crossref record; 3 of the 3 references it cites were found in a registry or an index.
The Relationship between Stochastic and Deterministic Models for Chemical Reactions
Abstract
The Markov chain and ordinary differential equation models for chemical reaction systems are compared. It is shown that if the volume of the reaction system is taken into account in an appropriate way in the formulation of the Markov chain model, then the o.d.e. model is the infinite volume limit of the Markov chain model. A central limit theorem is also given for the deviation of the Markov chain model from the o.d.e. model.
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Citations
Cites
Solutions of ordinary differential equations as limits of pure jump markov processes
Kurtz, T. G. (1970) · Journal of Applied Probability · doi:10.1017/s0021900200026929 · Cited by 947
Self-citationStochastic approach to chemical kinetics
McQuarrie, D. A. (1967) · Journal of Applied Probability · doi:10.1017/s002190020002547x · Cited by 917
Stochastic and Deterministic Formulation of Chemical Rate Equations
Oppenheim, I., Shuler, K. E., & Weiss, G. H. (1969) · The Journal of Chemical Physics · doi:10.1063/1.1670820 · Cited by 87
Cited by
Gillespie, D. T. (1976) · Journal of Computational Physics · doi:10.1016/0021-9991(76)90041-3 · Cited by 6,029
Approximate simulation of coupled fast and slow reactions for stochastic chemical kinetics
Haseltine, E. L., & Rawlings, J. B. (2002) · The Journal of Chemical Physics · doi:10.1063/1.1505860 · Cited by 565
Gaussian stochastic processes in physics
Fox, R. F. (1978) · Physics Reports · doi:10.1016/0370-1573(78)90145-x · Cited by 373
Toni, T., & Tidor, B. (2013) · PLoS Computational Biology · doi:10.1371/journal.pcbi.1002960 · Cited by 62
Dóka, É., & Lente, G. (2011) · Journal of the American Chemical Society · doi:10.1021/ja207408y · Cited by 60
Metadata
- Authors
- Kurtz, T. G.
- Venue
- The Journal of Chemical Physics
- Publisher
- AIP Publishing
- Published
- 1972-10-01
- Volume
- 57
- Issue
- 7
- Pages
- 2976-2978
- ISSN
- 0021-9606 (ISSN-L)
- 1089-7690
- OpenAlex
- W1976443948
- Cited by
- 536
- References
- 3
- FWCI
- 1.42
- Type
- journal article
- Language
- en
- Open access
- closed
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Data sources
Bibliographic data: Semantic Scholar, OpenAlex, Crossref.
Contains information from the Semantic Scholar Academic Graph Datasets, made available under the ODC Attribution License (ODC-BY 1.0).
Semantic Scholar’s data is described in: Kinney, R., et al. (2023). The Semantic Scholar Open Data Platform. arXiv:2301.10140.
