Essential sets and support sets for stochastic processes

Abstract

In recent articles the author used his work in measure and integration to produce a new universal concept of stochastic processes. This concept leads, for the first time, for a stochastic process to a natural notion of essential subsets in the path space. But there remained some contrast to the traditional treatment, for example because for the Poisson process the set of cadlag paths is not an essential subset. The present article is an attempt to harmonize the two approaches, in that it proposes and studies, for a stochastic process, besides the notion of essential sets the somewhat weaker but reasonable notion of support sets.