Существование и свойства локальных времен для марковских случайных полей

Abstract

Random fields that have the “coordinatewise” Markov property are considered. The notions of an excessive function, a potential, and a continuous additive functional are introduced. Sufficient conditions for the existence of local time as a special form of continuous additive functional are formulated, and the uniqueness of this time to within a multiplicative constant is proved.