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

Large deviations for random evolutions with independent increments in the scheme of the Poisson approximation


Author: I. V. Samoĭlenko
Translated by: N. Semenov
Original publication: Teoriya Imovirnostei ta Matematichna Statistika, tom 85 (2011).
Journal: Theor. Probability and Math. Statist. 85 (2012), 107-114
MSC (2010): Primary 60J55, 60B10, 60F17, 60K10; Secondary 60G46, 60G60
Published electronically: January 14, 2013
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Abstract: The asymptotic analysis of the large deviation problem for random evolutions with independent increments in the scheme of the Poisson approximation is performed. Large deviations for random evolutions in the scheme of the Poisson approximation are determined 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, National Academy of Science of Ukraine, Tereshchenkivs’ka Street, 3, Kyiv 01601, Ukraine
Email: isamoil@imath.kiev.ua

DOI: http://dx.doi.org/10.1090/S0094-9000-2013-00878-3
PII: S 0094-9000(2013)00878-3
Keywords: Large deviations, random evolution with independent increments, Poissonian approximation, exponential nonlinear operator
Received by editor(s): April 21, 2011
Published electronically: January 14, 2013
Additional Notes: The author would like to extend his sincere gratitude to Academician V. S. Koroliuk for the setting of the problem and for his constant help
Article copyright: © Copyright 2013 American Mathematical Society