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ON THE TIGHTNESS OF CAPACITIES ASSOCIATED WITH SUB-MARKOVIAN RESOLVENTS

Published online by Cambridge University Press:  12 December 2005

LUCIAN BEZNEA  and
NICU BOBOC
LUCIAN BEZNEA
Affiliation:
Institute of Mathematics ‘S. Stoilow’ of the Romanian Academy, P.O. Box 1-764, RO-014700 Bucharest, Romania, [email protected]
NICU BOBOC
Affiliation:
Faculty of Mathematics and Informatics, University of Bucharest, str. Academiei 14, RO-010014 Bucharest, Romania, [email protected]
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Abstract

This paper investigates the tightness property of the capacity induced by the reduction operator with respect to the resolvent of a right Markov process. Tightness is verified in two particular situations: under the ‘weak duality hypothesis’, and if a substitute for ‘the axiom of polarity for the dual theory’ holds. In the second context, the quasi-continuity property for the excessive functions is derived. These are extensions and improvements of results of Lyons and Röckner, Ma and Röckner, Le Jan, and Fitzsimmons, mainly obtained in the context of Dirichlet forms.

Keywords

31C2560J45 (primary)31C1560J40 (secondary)
Type
Papers
Information
Bulletin of the London Mathematical Society , Volume 37 , Issue 6 , December 2005 , pp. 899 - 907
Copyright
© The London Mathematical Society 2005

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