An equivalent Markov model for Gillespie's Stochastic Simulation Algorithm for biochemical systems

Mathematical/statistical modeling of biological systems is a desired goal for many years. It aims to be able to accurately predict the operation of such systems under various scenarios using computer simulations. In this paper we revisit Gillespie's Stochastic Simulation Algorithm for biochemical systems and we suggest an equivalent Markov Model for it. We show that under certain conditions it is a 1st order homogenous Markov process and we analyze these conditions. Our suggested model can be used to simulate the probability density function of a biochemical processes which, in turn, can be used for applying statistical signal processing and information theory tools on them.