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A note on the existence of transition probability densities of Lévy processes
-
Victoria Knopova
and
René L. Schilling
Published/Copyright:
January 3, 2013
Abstract.
We prove necessary and sufficient conditions for the existence of
(smooth) transition probability densities for Lévy processes and isotropic
Lévy processes. Under some mild conditions on the characteristic exponent we
calculate the asymptotic behaviour of the transition density as 
and 
and show a ratio-limit theorem.
Keywords: Transition probability density; absolute continuity; Hartman–Wintner condition; monotone rearrangement; anisotropic Sobolev spaces; volume doubling
Received: 2010-08-23
Revised: 2011-01-04
Published Online: 2013-01-03
Published in Print: 2013-01-01
© 2013 by Walter de Gruyter Berlin Boston
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Keywords for this article
Transition probability density;
absolute continuity;
Hartman–Wintner condition;
monotone rearrangement;
anisotropic Sobolev spaces;
volume doubling
Articles in the same Issue
- Masthead
- Isomorphism criteria for Witt rings of real fields
- Simplicial differential calculus, divided differences, and construction of Weil functors
- Rank 3 permutation characters and maximal subgroups
- On the oscillation and nonoscillation of the solutions of impulsive differential equations of second order with retarded argument
- A note on the existence of transition probability densities of Lévy processes
- Carleson measures and Logvinenko–Sereda sets on compact manifolds
- Cofiniteness of composed local cohomology modules
- Real hypersurfaces of type (A) in complex two-plane Grassmannians related to the commuting shape operator
- Deconstructibility and the Hill Lemma in Grothendieck categories
