Time reversal and stationary Gibbs measures
There exist many results saying that all time reversible stationary measures for an infinite particle system are Gibbsian with a potential determined by the transition mechanism. This paper gives an extension of this to the non reversible case with discrete time. The main result says that under some regularity conditions a stationary measure is Gibbs if and only if both the original and the time reversed transition kernels depend continuously on the initial values and then the potential is determined by these two kernels. The problem is somehow related to the problem of the global Markov property: One has to study the dependence of conditional distributions on the conditioning values when the available information is reduced. In continuous time similar but stronger results have been obtained in the author's paper ''Non reversible stationary measures for infinite interacting particle systems'', Z. Wahrscheinlichkeitstheor. Verw. Geb. 66, 407-424 (1984).
scientific article; zbMATH DE number 3852182