Preprint 41/1997

Conservativeness and extensions of Feller semigroups

Rene Schilling

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Submission date: 04. Dec. 1997
Pages: 19
published in: Positivity, 2 (1998) 3, p. 239-256 
DOI number (of the published article): 10.1023/A:1009748105208
MSC-Numbers: 47D07, 60J35, 47G30
Keywords and phrases: feller semigroup, feller process, conservativeness, positive maximum principle, pseudo-differential operator

Let img1 denote a Feller semigroup on the space of functions vanishing at infinity, img2, and img3 its (canonical) extension to the bounded measurable functions. We show that img4 is necessary and sufficient for the invariance of img5 under img3. If the generator of the semigroup is a pseudo-differential operator we can restate this condition in terms of the symbol. As a by-product, we obtain necessary and sufficient conditions for the conservativeness of the semigroup which are again expressed through the symbol.

29.11.2012, 16:37