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Compound kernel estimates for the transition probability density of a Lévy process in $ \mathbb{R}^n$


Author: Victoria Knopova
Original publication: Teoriya Imovirnostei ta Matematichna Statistika, tom 89 (2013).
Journal: Theor. Probability and Math. Statist. 89 (2014), 57-70
MSC (2010): Primary 60G51; Secondary 60J75, 41A60
DOI: https://doi.org/10.1090/S0094-9000-2015-00935-2
Published electronically: January 26, 2015
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Abstract: We construct in the small-time setting the upper and lower estimates for the transition probability density of a Lévy process in $ \mathbb{R}^n$. Our approach relies on the complex analysis technique and the asymptotic analysis of the inverse Fourier transform of the characteristic function of the process.


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Additional Information

Victoria Knopova
Affiliation: V. M. Glushkov Institute of Cybernetics, National Academy of Science of Ukraine, 40, Academician Glushkov Avenue, 03187, Kyiv, Ukraine
Email: vic_knopova@gmx.de

DOI: https://doi.org/10.1090/S0094-9000-2015-00935-2
Keywords: Transition probability density, transition density estimates, L\'evy processes, Laplace method
Received by editor(s): June 1, 2013
Published electronically: January 26, 2015
Article copyright: © Copyright 2015 American Mathematical Society