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A family of symmetric stable-like processes and its global path properties

Isozaki Y., Uemura T.

Probability and Mathematical Statistics

2004

Vol. 24, Fasc. 1

145--164

We extend the idea of the symmetric stable-like processes so that it includes the Brownian motion as well as the symmetric α-stable processes. We exhibit some sufficient conditions for their recurrence and conservativeness relying on the no-tion of Dirichlet forms. A criterion for conservativeness (Lemma 3.2) is also shown in terms of general Dirichlet forms and the associated generators.