The slow-scale stochastic simulation algorithm

Journal of Chemical Physics

Volumn 122, Issue 1, 2005, Pages

  Cao, Yang ^a,b   Gillespie, Daniel T ^a,b   Petzold, Linda R ^a  

^a University of California   (United States)

^b Dan T Gillespie Consulting   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

CHEMICAL SYSTEMS; DYNAMICAL STIFFNESS; REACTION CHANNELS; STOCHASTIC SIMULATION ALGORITHMS;

ALGORITHMS; APPROXIMATION THEORY; COMPUTER SIMULATION; RANDOM PROCESSES; STIFFNESS; THEOREM PROVING;

REACTION KINETICS;

EID: 22944480262     PISSN: 00219606     EISSN: None     Source Type: Journal    
DOI: 10.1063/1.1824902     Document Type: Article

References (15)

1. D. T. Gillespie, J. Comput. Phys. 22, 403 (1976);
2. J. Phys. Chem. 81, 2340 (1977);
3. Physica A 188, 404 (1992).
4. E. L. Haseltine and J. B. Rawlings, J. Chem. Phys. 117, 6959 (2002).
5. C. V. Rao and A. P. Arkin, J. Chem. Phys. 118, 4999 (2003).
6. all yPr{Y(∞)=y}y.
7. M. Rathinam, L. R. Petzold, Y. Cao, and D. T. Gillespie, J. Chem. Phys. 119, 12784 (2003).
8. D. T. Gillespie, J. Chem. Phys. 115, 1716 (2001);
9. D. T. Gillespie and L. R. Petzold, 119, 8229 (2003).
10. A. Arkin, J. Ross, and H. H. McAdams, Genetics 149, 1633 (1998).
11. s(t) separately do not satisfy such an equation, so they are not Markovian. References 2 and 3 take for their fast process the (real) fast process conditioned on the slow process. That process is shown in Ref. 3 to satisfy its Eq. (5) - an equation that almost has the canonical form of our Eq. (5), but not quite; it falls short in that the slow variables in the two propensity functions on the right-hand side have different values. This implies that the fast process conditioned on the slow process is not Markovian. To carry out a proper analysis of a non-Markovian process on its own terms - i.e., without first "embedding" it in a larger Markov process and then analyzing that larger process - is horrendously difficult, largely because one must ensure the simultaneous satisfaction of infinitely many coupled integral equations;
12. see D. Gillespie, W. Alltop, and J. Martin, Chaos 11, 548 (2001).
13. H. Kurata, H. El-Samad, T.-M. Yi, J. Khammash, and J. Doyle, in Proceedings of the 40th IEEE Conference on Decision and Control, 2001 (unpublished).
14. J. Doyle (private communication).
15. D. T. Gillespie, Markov Processes: An Introduction for Physical Scientists (Academic, San Diego, 1992). See especially Sec. 6.4 and Appendix D; in the latter it is shown that the "effective width" of a Gaussian peak is 2π times the standard deviation.