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

MathSciNet review:
2933707

Full-text PDF

Abstract | References | Similar Articles | Additional Information

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:
https://doi.org/10.1090/S0094-9000-2013-00878-3

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