A FAMILY OF SYMMETRIC STABLE-LIKE PROCESSES AND ITS
GLOBAL PATH PROPERTIES
Yasuki Isozaki
Toshffliro Uemura
Abstract: We extend the idea of the symmetric stable-like processes so that it includes the
Brownian motion as well as the symmetric -stable processes. We exhibit some sufficient
conditions for their recurrence and conservativeness relying on the notion of Dirichlet forms.
A criterion for conservativeness (Lemma 3.2) is also shown in terms of general Dirichlet
forms and the associated generators.
2000 AMS Mathematics Subject Classification: 60J7S, 60G17.
Key words and phrases: Stable-like processes, recurrence, transience.