Error analysis of tau-leap simulation methods

Annals of Applied Probability

Volumn 21, Issue 6, 2011, Pages 2226-2262

  Anderson, David F ^a   Ganguly, Arnab ^b   Kurtz, Thomas G ^a  

^a UNIVERSITY OF WISCONSIN MADISON   (United States)

^b ETH ZURICH   (Switzerland)

Author keywords

Chemical master equation; Error analysis; Markov chain; Reaction networks; Simulation; Tau leaping

Indexed keywords

EID: 79957948210     PISSN: 10505164     EISSN: None     Source Type: Journal    
DOI: 10.1214/10-AAP756     Document Type: Article

References (19)

1. ANDERSON, D. F. (2007). A modified next reaction method for simulating chemical systems with time dependent propensities and delays. J. Chem. Phys. 127 214107.
2. ANDERSON, D. F. (2008). Incorporating postleap checks in tau-leaping. J. Chem. Phys. 128 054103.
3. CAO, Y., GILLESPIE, D. T. and PETZOLD, L. R. (2005). Avoiding negative populations in explicit Poisson tau-leaping. J. Chem. Phys. 123 054104.
4. CAO, Y., GILLESPIE, D. T. and PETZOLD, L. R. (2006). Efficient step size selection for the tau-leaping simulation method. J. Chem. Phys. 124 044109.
5. CHATTERJEE, A.,VLACHOS, D. G. andKATSOULAKIS, M. A. (2005). Binomial distribution based tau-leap accelerated stochastic simulation. J. Chem. Phys. 122 024112.
6. ETHIER, S. N. and KURTZ, T. G. (1986). Markov Processes: Characterization and Convergence. Wiley, New York. MR0838085
7. ETHIER, S. N. and KURTZ, T. G. (2005). Markov Processes: Characterization and Convergence, 2nd ed. Wiley, New York.
8. GIBSON, M. A. and BRUCK, J. (2000). Efficient exact stochastic simulation of chemical systems with many species and many channels. J. Phys. Chem. A 105 1876-1889.
9. GILLESPIE, D. T. (1976). A general method for numerically simulating the stochastic time evolution of coupled chemical reactions. J. Comput. Phys. 22 403-434. MR0503370
10. GILLESPIE, D. T. (1977). Exact stochastic simulation of coupled chemical reactions. J. Phys. Chem. 81 2340-2361.
11. GILLESPIE, D. T. (2001). Approximate accelerated simulation of chemically reaction systems. J. Chem. Phys. 115 1716-1733. (Pubitemid 32715518)
12. GILLESPIE, D. T. and PETZOLD, L. R. (2003). Improved leap-size selection for accelerated stochastic simulation. J. Chem. Phys. 119 8229-8234.
13. KLOEDEN, P. E. and PLATEN, E. (1992). Numerical Solution of Stochastic Differential Equations. Applications of Mathematics (New York) 23. Springer, Berlin. MR1214374
14. KURTZ, T. G. (1972). The relationship between stochastic and deterministic models for chemical reactions. J. Chem. Phys. 57 2976-2978.
15. KURTZ, T. G. (1977/78). Strong approximation theorems for density dependent Markov chains. Stochastic Processes Appl. 6 223-240. MR0464414
16. KURTZ, T. G. (1981). Approximation of Population Processes. CBMS-NSF Regional Conference Series in Applied Mathematics 36. SIAM, Philadelphia, PA. MR0610982
17. LI, T. (2007). Analysis of explicit tau-leaping schemes for simulating chemically reacting systems. Multiscale Model. Simul. 6 417-436 (electronic). MR2338489
18. RATHINAM, M., PETZOLD, L. R., CAO, Y. and GILLESPIE, D. T. (2005). Consistency and stability of tau-leaping schemes for chemical reaction systems. Multiscale Model. Simul. 4 867-895 (electronic). MR2203944 (Pubitemid 44340291)
19. WILKINSON, D. J. (2006). Stochastic Modelling for Systems Biology. Chapman and Hall/CRC, Boca Raton, FL. MR2222876