MASTER-EQUATION APPROACH TO STOCHASTIC NEURODYNAMICS

A master-equation approach to the stochastic neurodynamics proposed by Cowan [in Advances in Neural Information Processing Systems 3, edited by R. P. Lippman, J. E. Moody, and D. S. Touretzky (Morgan Kaufmann, San Mateo, 1991), p. 62] is investigated in this paper. We deal with a model neural network that is composed of two-state neurons obeying el ementary stochastic transition rates. We show that such an approach yi elds concise expressions for multipoint moments and an equation of mot ion. We apply the formalism to a (1 + 1)-dimensional system. Exact and approximate expressions for various statistical parameters are obtain ed and compared with Monte Carlo simulations.