Positivity

, Volume 2, Issue 3, pp 239–256

Conservativeness and Extensions of Feller Semigroups

  • René L. Schilling
Article

DOI: 10.1023/A:1009748105208

Cite this article as:
Schilling, R.L. Positivity (1998) 2: 239. doi:10.1023/A:1009748105208

Abstract

Let \(\{ T_t \} _{t \geqslant 0} \) denote a Feller semigroup on \(C_\infty (\mathbb{R}^n )\), and \(\{ \tilde T_t \} _{t \geqslant 0} \) itsextension to the bounded measurable functions. We show that\(T_t 1 \in C_b (\mathbb{R}^n )\). 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.

Feller semigroup; Feller process;conservativeness; positive maximum principle; pseudo-differential operator 

Copyright information

© Kluwer Academic Publishers 1998

Authors and Affiliations

  • René L. Schilling
    • 1
  1. 1.Max-Planck-Institut für Mathematik in den NaturwissenschaftenLeipzigGermany

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