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Law of the iterated logarithm for solutions of stochastic equations


Authors: D. S. Budkov and S. Ya. Makhno
Translated by: O. Klesov
Original publication: Teoriya Imovirnostei ta Matematichna Statistika, tom 83 (2010).
Journal: Theor. Probability and Math. Statist. 83 (2011), 47-57
MSC (2010): Primary 60F10, 60F17
Published electronically: February 2, 2012
MathSciNet review: 2768847
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Abstract | References | Similar Articles | Additional Information

Abstract: Strassen's law of the iterated logarithm for a solution $ x(t)$ of Itô's stochastic equation is considered in the paper. We obtain a result for small times in the uniform metric and for a more general normalizing function than the classical $ \sqrt { h\ln \ln \frac {1}{h}}$.


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Additional Information

D. S. Budkov
Affiliation: Department of Probability Theory and Mathematical Statistics, Institute of Applied Mathematics and Mechanics, National Academy of Sciences of Ukraine, R. Luxemburg Street 74, Donetsk 83114, Ukraine
Email: budkov@iamm.ac.donetsk.ua

S. Ya. Makhno
Affiliation: Department of Probability Theory and Mathematical Statistics, Institute of Applied Mathematics and Mechanics, National Academy of Sciences of Ukraine, R. Luxemburg Street 74, Donetsk 83114, Ukraine
Email: makhno@iamm.ac.donetsk.ua

DOI: https://doi.org/10.1090/S0094-9000-2012-00840-5
Keywords: Stochastic equation, large deviations, law of the iterated logarithm
Received by editor(s): December 10, 2009
Published electronically: February 2, 2012
Additional Notes: The research is supported by the Foundation for Joint Scientific Researches of National Academy of Science of Ukraine and Russian Foundation for Fundamental Researches, grant #104
Article copyright: © Copyright 2012 American Mathematical Society