Introduction to the Theory of Dirichlet Forms

the long version

The purpose of this book is to give a streamlined introduction to the theoryof (not necessarily symmetric) Dirichlet forms on general state spaces. It includes both the analytic and probabilistic components of the theory. Asubstantial part of the book is designed for a one-year graduate course: it provides a framework which covers both the well-studied "classical" theory of regular Dirichlet forms on locally compact state spaces and all recent extensions to infinite-dimensional state spaces. Among other things it contains a complete proof of an analytic characterization of the class of Dirichlet forms which are associated with right continuous strong Markov processes, i.e., those having a probabilistic counterpart. This solves a long-standing open problem of the theory. Finally, a general regularization method is developedwhich makes it possible to transfer all results known in the classical locally compact regular case to this (in the above sense) most general classof Dirichlet forms.