A RANDOM-FIELD APPROACH TO WEAK-CONVERGENCE OF PROCESSES

Abstract

Random fields in J'(R(d+1)) are associated to processes with paths in D([0, 1], J'(R(d))). This embedding provides a way to analyze weak convergence for such processes. The approach is also useful for real valued processes. The idea is to regard processes as time random fields. The method is illustrated with the fluctuations of an infinite particle system.