Construction by subordination of processes with jumps on infinite dimensional state spaces and corresponding non local Dirichlet forms (Q2702420)

The authors use subordination in the sense of Bochner to construct symmetric non-local quasi-regular Dirichlet forms on infinite-dimensional state spaces. They consider any symmetric Markov semigroup on \(L^2(X, m)\), \((X,m)\) is some measure space, which is then subordinated with respect to a Bernstein function. A concrete representation for the subordinate generator is given and its cores and domain are characterized. It is shown that closability and quasi-regularity of the associated Dirichlet forms as well as the (essential) self-adjointness of their generators is hereditary under subordination. The results are then applied in order to construct jump-type processes and to subordinate the infinite-dimensional Ornstein-Uhlenbeck process.NEWLINENEWLINEFor the entire collection see [Zbl 0953.00049].