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Large deviations problem for random evolution processes


Authors: V. S. Koroliuk and I. V. Samoilenko
Translated by: S. Kvasko
Original publication: Teoriya Imovirnostei ta Matematichna Statistika, tom 93 (2015).
Journal: Theor. Probability and Math. Statist. 93 (2016), 93-101
MSC (2010): Primary 60J55, 60B10, 60F17, 60K10; Secondary 60G46, 60G60
DOI: https://doi.org/10.1090/tpms/996
Published electronically: February 7, 2017
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Abstract: This is a short survey of the joint author results concerning the large deviations problem for some stochastic processes of random evolution published in the papers [5]-[20].


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Additional Information

V. S. Koroliuk
Affiliation: Institute of Mathematics, National Academy of Science of Ukraine, Tereshchenkivs’ka Street, 3, Kyiv 01601, Ukraine
Email: vskorol@yahoo.com

I. V. Samoilenko
Affiliation: Faculty for Computer Science and Cybernetics, National Taras Shevchenko University, Academician Glushkov Avenue, 4, Kyiv 03127, Ukraine
Email: isamoil@i.ua

DOI: https://doi.org/10.1090/tpms/996
Keywords: Large deviations, random evolution processes, asymptotically small diffusion, L\'evy approximation, exponential nonlinear generator, split and double merging
Received by editor(s): June 29, 2015
Published electronically: February 7, 2017
Additional Notes: This paper was prepared following the talk at the International conference “Probability, Reliability and Stochastic Optimization (PRESTO-2015)” held in Kyiv, Ukraine, April 7–10, 2015
Article copyright: © Copyright 2017 American Mathematical Society