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Theory of Probability and Mathematical Statistics

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Large deviations for solutions of one dimensional Itô equations


Author: A. V. Logachov
Translated by: N. Semenov
Original publication: Teoriya Imovirnostei ta Matematichna Statistika, tom 90 (2014).
Journal: Theor. Probability and Math. Statist. 90 (2015), 127-137
MSC (2010): Primary 60F10, 60F17
DOI: https://doi.org/10.1090/tpms/954
Published electronically: August 10, 2015
MathSciNet review: 3242025
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Abstract: The large deviations principle for the sequence of stochastic processes

$\displaystyle \eta _n(t)=x_0+\int _0^t b(n\eta _n(s))\,ds+\frac {1}{\varphi (n)}\int _0^t \sigma (n\eta _n(s))\,dw(s) $

is proved if the limits of integral means exist for the functions $ b(x)\sigma ^{-2}(x)$ and $ \sigma ^{-2}(x)$. The rate functional is evaluated.

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Additional Information

A. V. Logachov
Affiliation: Department of Probability Theory and Mathematical Statistics, Institute for Applied Mathematics and Mechanics, National Academy of Science of Ukraine, R. Luxemburg Street, 74, Donetsk, 83114, Ukraine
Email: omboldovskaya@mail.ru

DOI: https://doi.org/10.1090/tpms/954
Keywords: Large deviations, rate functional, stochastic differential equation
Received by editor(s): November 15, 2012
Published electronically: August 10, 2015
Article copyright: © Copyright 2015 American Mathematical Society