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Large deviations for impulsive processes in the scheme of the Lévy approximation


Author: I. V. Samoĭlenko
Translated by: N. Semenov
Original publication: Teoriya Imovirnostei ta Matematichna Statistika, tom 88 (2013).
Journal: Theor. Probability and Math. Statist. 88 (2014), 151-160
MSC (2010): Primary 60J55, 60B10, 60F17, 60K10; Secondary 60G46, 60G60
DOI: https://doi.org/10.1090/S0094-9000-2014-00925-4
Published electronically: July 24, 2014
MathSciNet review: 3112641
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Abstract: Asymptotic analysis of the large deviations problem for impulsive processes in the scheme of the Lévy approximation is realized. Large deviations for impulsive processes in the scheme of the Lévy approximation are defined by the exponential generator for a jump process with independent increments.


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Additional Information

I. V. Samoĭlenko
Affiliation: Department of Fractal Analysis, Institute of Mathematics of National Academy of Science of Ukraine, Tereshchenkivs’ka Street, 3, Kyiv 01601, Ukraine
Email: isamoil@imath.kiev.ua

DOI: https://doi.org/10.1090/S0094-9000-2014-00925-4
Keywords: Large deviations, impulsive process, L\'evy approximation, exponential nonlinear operator
Received by editor(s): October 10, 2012
Published electronically: July 24, 2014
Additional Notes: The author is grateful to Academician of the National Academy of Science of Ukraine V. S. Koroliuk for posing the problem and for constant attention to its implementation
Article copyright: © Copyright 2014 American Mathematical Society