Introduction to stochastic simulation
with the Gillespie method

David Karig

Department of Electrical Engineering
Princeton University

Many systems are driven by random, discrete interactions.  In chemical systems, molecules randomly collide and react with a certain probability.  Similarly, biological networks are characterized by discrete interactions between DNA, proteins, and other chemicals.  In other areas such as finance and epidemiology, systems are driven by probabilistic interactions between people.  In many cases, traditional deterministic simulations do not realistically depict the behavior of such processes.  In 1976, Gillespie developed a computational method for the exact stochastic simulation of coupled ordinary differential equations (1, 2). With the dramatic increase in computing power over the past decades this method now provides an appealing complementary approach to the standard deterministic formulation for many problems.  This talk will serve as a tutorial introduction to Gillespie's stochastic simulation algorithm.

1. Gillespie D.T., (1976), "A General Method for Numerically Simulating the Stochastic Time Evolution of Coupled Chemical Reactions," J.Comp. Phys., 22:403-434.
    

2. Gillespie D.T., (1977), "Exact Stochastic Simulation of Coupled Chemical Reactions," J. Phys. Chem., 81:2340-2361.