# Bibliography

Books.

- An Introduction to Stochastic Models with Applications to Biology by Linda Allen
- Introduction to Algorithms, Second Edition. by Thomas H. Cormen, Charles E. Leiserson, Ronald L. Rivest, and Clifford Stein.
- Non-Uniform Random Variate Generation by Luc Devroye.
- Markov Processes: An Introduction for Physical Scientists by Daniel T. Gillespie. Academic Press, Boston, 1992.
- Stochastic Approaches for Systems Biology by Mukhtar Ullah and Olaf Wolkenhauer.
- Stochastic Modelling for Systems Biology by Darren Wilkinson.

Articles.

- Yang Cao, Hong Li, and Linda Petzold "Efficient formulation of the stochastic simulation algorithm for chemically reacting systems." Journal of Chemical Physics, Vol. 121, No. 9, 2004.
- Yang Cao, Daniel T. Gillespie, and Linda Petzold "Efficient step size selection for the tau-leaping simulation method" Journal of Chemical Physics, Vol. 124, 2006.
- Yang Cao and Linda Petzold "Accuracy limitations and the measurement of errors in the stochastic simulation of chemically reacting systems." Journal of Computational Physics, Vol. 212, 2006, 6-24.
- Michael A. Gibson and Jehoshua Bruck. "Efficient Exact Stochastic Simulation of Chemical Systems with Many Species and Many Channels." Journal of Physical Chemistry A, Vol. 104, No. 9, 1876-1889, 2000.
- Daniel T. Gillespie "A General Method for Numerically Simulating the Stochastic Time Evolution of Coupled Chemical Reactions", Journal of Computational Physics, Vol. 22, No. 4, 1976, 403-434.
- Daniel T. Gillespie "Exact Stochastic Simulation of Coupled Chemical Reactions." Journal of Physical Chemistry, Vol. 81, No. 25, 1977.
- Daniel T. Gillespie "Stochastic Simulation of Chemical Kinetics" Annu. Rev. Phys. Chem., Vol. 58, 2007, 35-55.
- Andrzej M. Kierzek "STOCKS: STOChastic Kinetic Simulations of biochemical systems with the Gillespie algorithm" Bioinformatics, Vol. 18, No. 3, 2002, 470-481.
- Hong Li and Linda Petzold "Logarithmic Direct Method for Discrete Stochastic Simulation of Chemically Reacting Systems". Department of Computer Science, University of California, Santa Barbara, 2006.
- Azi Lipshtat ""All possible steps" approach to the accelerated use of Gillespie's algorithm" Journal of Chemical Physics, Vol. 126, No. 18, 2007.
- M. Matsumoto and T. Nishimura "Mersenne Twister: A 623-dimensionally equidistributed uniform pseudorandom number generator." ACM Trans. on Modelling and Computer Simulation, Vol. 8, No. 1, Jan. 1998, 3-30.
- George Marsaglia and Wai Wan Tsang. "The ziggurat method for generating random variables." Journal of Statistical Software, Vol. 5, 2000, Issue 8. http://www.jstatsoft.org/v05/i08/
- Sean Mauch and Mark Stalzer, "An efficient method for computing steady state solutions with Gillespie's direct method," Journal of Chemical Physics, Vol. 133, Iss. 14, Num. 144108, Oct. 14, 2010.
- Sean Mauch and Mark Stalzer, "Efficient Formulations for Exact Stochastic Simulation of Chemical Systems," IEEE/ACM Transactions on Computational Biology and Bioinformatics, pp. 27-35, January-February, 2011.
- James M. McCollum, Gregory D. Peterson, Chris D. Cox, Michael L. Simpson, and Nagiza F. Samatova "The sorting direct method for stochastic simulation of biochemical systems with varying reaction execution behavior." Computational Biology and Chemistry, Vol. 30, No. 1, Feb. 2006, 39-49.
- C. J. Proctor, C. Soti, R. J. Boys, C. S. Gillespie, D. P. Shanley, D. J. Wilkinson, and T. B. L. Kirkwood "Modelling the actions of chaperones and their role in ageing" Mechanisms of Ageing and Development, Vol. 126, No. 1, Jan. 2005, 119-131.
- Herman Rubin and Brad Johnson. "Efficient generation of exponential and normal deviates." Journal of Statistical Computation and Simulation, Vol. 76, No. 6, 509-518, 2006.
- M. Sehl, A. V. Alekseyenko, K. L. Lange "Accurate Stochastic Simulation via the Step Anticipation tau-Leaping (SAL) Algorithm" Journal of Computational Biology, Vol. 16, Iss. 9, 1195-1208, Sep. 2009.
- Alexander Slepoy, Aidan P. Thompson, and Steven J. Plimpton "A constant-time kinetic Monte Carlo algorithm for simulation of large biochemical reaction networks" Journal of Chemical Physics, Vol. 128, No. 20, 2008.