Efficient numerical schemes for stochastic chemical kinetics (Correction)

Muruhan Rathinam
Dept. of Mathematics and Statistics
University of Maryland, Baltimore County

ABSTRACT:
In general many chemically reacting molecular systems are modeled by
deterministic and continuous models using ODEs or PDEs.  However there are certain situations when the continuous and deterministic models are inadequate. Prime examples are intra-cellular gene transcription mechanisms where the fluctuations of certain molecular species present in very low numbers may have a critical effect on the final state of the system.

On a microscopic level molecular reactions may be modeled by continuous time discrete state Markov processes. In principle such a process can be simulated exactly by keeping track of each random jump event.  This accurate method however would take prohibitively long computing time for most real problems. In this talk we describe an ongoing project which aims to develop methods, software, and rigorous mathematical theory for simulating these systems in an efficient way by ``leaping over'' several events at a time. We address certain important issues such as stiffness and preserving nonnegativity of states.

More broadly these schemes would be applicable to other situations such as the dynamics of market microstructures and traffic models where the detailed models are discrete and stochastic.