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On Certain Extensions of a Rotation Invariant Markov Process
Authors:Juha Vuolle-Apiala
Institution:(1) Department of Mathematics and Statistics, University of Vaasa, P.O. Box 700, 65101 Vaasa, Finland
Abstract:Let (X t ,P x ) be a rotation invariant (RI) Feller process on R d setmn{0}, dge2. We study certain type of strong Markov extensions of (X t ,P x ) to R d . It turns out that that the unique (RI) extension always exists and is of that type. We give a kind of quasi-ergodicy condition (E) under which the (RI) extension is the only extension of that type. A class of processes fulfilling (E) is also characterized.
Keywords:Markov process  excursion theory  entrance law  rotation invariant  Feller process  skew product
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