Continuous Stochastic Cellular Automata that Have a Stationary Distribution and No Detailed Balance

Abstract

Marroquin and Ramirez (1990) have recently discovered a class of discrete stochastic cellular automata with Gibbsian invariant measures that have a non-reversible dynamic behavior. Practical applications include more powerful algorithms than the Metropolis algorithm to compute MRF models. In this paper we describe a large class of stochastic dynamical systems that has a Gibbs asymptotic distribution but does not satisfy reversibility. We characterize sufficient properties of a sub-class of stochastic differential equations in terms of the associated Fokker-Planck equation for the existence of an asymptotic probability distribution in the system of coordinates which is given. Practical implications include VLSI analog circuits to compute coupled MRF models.