Conditions for the existence and smoothness of the distribution density of the Ornstein–Uhlenbeck process with Lévy noise

Bodnarchuk, S.; Kulyk, O.

doi:10.1090/S0094-9000-09-00778-9

Conditions for the existence and smoothness of the distribution density of the Ornstein–Uhlenbeck process with Lévy noise

Authors: S. V. Bodnarchuk and O. M. Kulyk
Translated by: S. Kvasko
Journal: Theor. Probability and Math. Statist. 79 (2009), 23-38
MSC (2000): Primary 60J75, 60E99, 60H10
DOI: https://doi.org/10.1090/S0094-9000-09-00778-9
Published electronically: December 29, 2009
MathSciNet review: 2494533
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: Some sufficient conditions are found for the distribution of the Ornstein–Uhlenbeck process with Lévy noise to be absolutely continuous or to have a smooth density. These conditions are necessary for one-dimensional processes with a nondegenerate drift coefficient. We also give a multidimensional analog of the condition that the drift parameter is nondegenerate.

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