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 1^st 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.