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Sergio Albeverio, Barbara Rdiger

Subordination of symmetric quasi -regular Dirichlet forms

Keywords: Infinite dimensional, stochastic differential equations, stochastic partial differential equations, subordination, pseudo -differential operators, Dirichlet forms, uniqueness

The generators of subordinate symmetric (sub-) Markov processes and their domains are exhibited by using spectral theory. The construction preserves sets of essential self -adjointness of the generators.

General non local symmetric quasi regular Dirichlet forms and the corresponding processes (with jumps) are shown to be constructible by subordination of processes properly associated to symmetric quasi regular Dirichlet forms (in particular local ones). It is proven that subordination preserves the property of a process to be a symmetric m -tight special standard process. A characterization of the subordinate processes in terms of solutions of the corresponding martingale problems is obtained.

Random Operators and Stochastic Equations, Walter de Gruyter

Print ISSN: 0926-6364
Volume: 13, 01/2005
Pages: 17 - 38

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