An Optimal Final State Projection Method

Abstract

It is well known that many realistic mathematical models of biological and chemical systems, such as enzyme cascades and gene regulatory networks, need to include stochasticity. These systems can be described as Markov processes and are modelled using the Chemical Master Equation (CME). The CME is a differential-difference equation (continuous in time and discrete in the state space) for the probability of certain state at a given time. The state space is the population count of species in the system. A successful method for computing the CME is the Finite State Projection Method (FSP). In this paper we will give the mathematical background of the FSP and propose a new addition to the FSP which guaranties our approximation to have optimal order. Show more