A COMPUTATIONAL METHOD FOR COARSE-GRAINED STATIONARY DISTRIBUTIONS OF THE MASTER EQUATION

A computational method is introduced for calculating coarse-grained stationary distributions of stochastic systems formulated by the master equation. By coarse-graining the state space, it becomes possible to enlarge the size of systems without increasing the number of calculation procedures. As a result, we will be free from the difficulty of the limitation on the system size. Therefore the method makes it practicable to numerically analyze statistical properties of nonlinear stochastic systems large enough for appraising the state of systems in the thermodynamic limit. Furthermore, it becomes easy to study the spatial structure of fluctuations of stochastic systems.