2010 年 9 巻 3 号 p. 135-142
The aim of this paper is to investigate the discrete nature of chemically reacting systems. In order to achieve our purpose we propose a systematic method to compare the discrete stochastic model of chemically reacting systems with the continuous stochastic model. We adopt the chemical master equation (CME) as the discrete stochastic model and the chemical Fokker-Planck equation (CFPE) as the continuous stochastic model. By making use of the well-known idea of approximating diffusion processes by birth-death processes, we construct a family of master equations parameterized by the degree of discreteness. This family of master equations bridges CME and CFPE. With full degree of discreteness we obtain CME and as decreasing discreteness the family of master equations converges to CFPE. Our strategy is not to study CME directly but to distinguish the properties of CME by putting CME into the family of master equations bridging CME and CFPE. We examine the usefulness of our construction by two simple examples.
