Markov Processes Associated With Positivity Preserving Coercive Forms

Abstract

Abstract Coercive closed forms on L 2 -spaces are studied whose associated L 2 -semigroups are positivity preserving. Earlier work by other authors is extended by further developing the potential theory of such forms and completed by proving an analytic characterization of those of these forms which have a probabilistic counterpart, i.e. , are associated with (special standard) Markov processes. Examples with finite and infinite dimensional state spaces are discussed.