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Theory of Probability and Mathematical Statistics
Theory of Probability and Mathematical Statistics
ISSN 1547-7363(online) ISSN 0094-9000(print)

 

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
Original publication: Teoriya Imovirnostei ta Matematichna Statistika, tom 79 (2008).
Journal: Theor. Probability and Math. Statist. 79 (2009), 23-38
MSC (2000): Primary 60J75, 60E99, 60H10
Published electronically: December 29, 2009
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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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Additional Information

S. V. Bodnarchuk
Affiliation: National Taras Shevchenko University, Academician Glushkov Avenue 6, Kyiv 03127, Ukraine
Email: sem_bodn@ukr.net

O. M. Kulyk
Affiliation: Institute of Mathematics, National Academy of Sciences of Ukraine, Tereshchenkivs’ka Street 3, Kyiv 01601, Ukraine
Email: kulik@imath.kiev.ua

DOI: http://dx.doi.org/10.1090/S0094-9000-09-00778-9
PII: S 0094-9000(09)00778-9
Keywords: Linear stochastic differential equation, L\'evy process, distribution density
Received by editor(s): May 19, 2008
Published electronically: December 29, 2009
Additional Notes: Supported by the Ministry of Education and Science of Ukraine, project GP/F26/0106
Article copyright: © Copyright 2009 American Mathematical Society