Solving the chemical master equation for monomolecular reaction systems analytically

Alfonsi A., Cancès E., Turinici G., Ventura B.D., Huisinga W. (2005) Adaptive simulation of hybrid stochastic and deterministic models for biochemical systems. ESAIM Proc. 14, 1–13

Anderson D.H. (1983) Compartmental Modeling and Tracer Kinetics. Number 50 in Lecture Notes in Biomathematics. Springer, Berlin Heidelberg New York

Burrage, K., Tian, T.: Poisson Runge–Kutta methods for chemical reaction systems. In: Proceedings of the Hong Kong Conference on Scientific Computing, 2003 (in press).

Burrage K., Tian T., Burrage P. (2004) A multi-scaled approach for simulating chemical reaction systems. Prog. Biophy. Mol. Biol. 85, 217–234

Cao Y., Gillespie D., Petzold L. (2005) The slow-scale stochastic simulation algorithm. J. Chem. Phys. 122(1): 014116

Darvey I., Staff P. (1966) Stochastic approach to first-order chemical reaction kinetics. J. Chem. Phys. 44(3): 990–997

Fall C.P., Marland E.S., Wagner J.M., Tyson J.J. (2002) Computational Cell Biology, volume 20 of Interdisciplinary Applied Mathematics. Springer, Berlin Heidelberg New York

Gadgil C., Lee C.-H., Othmer H.G. (2005) A stochastic analysis of first-order reaction networks. Bull. Math. Biol. 67, 901–946

Gardiner C.W. (1985) Handbook of Stochastic Methods. Springer, Berlin Heidelberg New York, , 2nd enlarged edition

Gibson M.A., Bruck J. (2000) Efficient exact stochastic simulation of chemical systems with many species and many channels. J. Phys. Chem. A 104, 1876–1889

Gillespie D.T. (1976) A general method for numerically simulating the stochastic time evolution of coupled chemical reactions. J. Comput. Phys. 22, 403–434

Gillespie D.T. (2001) Approximate accelerated stochastic simulation of chemically reacting systems. J. Chem. Phys. 115 (4): 1716–1733

Gillespie D.T. (2002) The chemical Langevin and Fokker–Planck equations for the reversible isomerization reaction. J. Phys. Chem. 106, 5063–5071

Golberg M.A. (1984) An Introduction to Probability Theory with Statistical Applications. Plenum Press, New York and London

Haseltine E.L., Rawlings J.B. (2002) Approximate simulation of coupled fast and slow reactions for stochastic chemical kinetics. J. Chem. Phys. 117 (15): 6959–6969

Iserles A., Nørsett S.P. (1999) On the solution of lienar differential equations in Lie groups. Philos. Trans. R. Soc. Lond., Ser. A, Math. Phys. Eng. Sci. 357(1754): 983–1019

Kotz, S. Johnson, N.L., Read, C.B.: editors. Encyclopedia of Statistical sciences, vol. 5. Wiley, New York, Chichester, Brisbane, Toronto, Singapore (1985)

Lang S. (1987) Linear algebra. Undergraduate Texts in Mathematics, 3rd edn. Springer, Berlin Heidelberg New York

Rao C.V., Arkin A.P. (2003) Stochastic chemical kinetics and the quasi-steady-state assumption: application to the Gillespie algorithm. J. Chem. Phys. 118(11): 4999–5010

Salis H., Kaznessis Y. (2005) Accurate hybrid simulation of a system of coupled chemical or biochemical reactions. J. Chem. Phys. 122

Todorovic P. (1992) An Introduction to Stochastic Processes and their Applications. Springer, Berlin Heidelberg New York

Turner T.E., Schnell S., Burrage K. (2004) Stochastic approaches for modelling in vivo reactions. Comput. Biol. Chem. 28, 165–178