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

Published electronically:
August 10, 2015

MathSciNet review:
3242025

Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: The large deviations principle for the sequence of stochastic processes

**1.**Mark I. Freidlin and Richard B. Sowers,*A comparison of homogenization and large deviations, with applications to wavefront propagation*, Stochastic Process. Appl.**82**(1999), no. 1, 23–52. MR**1695068**, 10.1016/S0304-4149(99)00003-4**2.**S. Ya. Makhno,*Large deviations for solutions of stochastic equations*, Teor. Veroyatnost. i Primenen.**40**(1995), no. 4, 764–785 (Russian, with Russian summary); English transl., Theory Probab. Appl.**40**(1995), no. 4, 660–678 (1996). MR**1405144**, 10.1137/1140076**3.**A. D. Wentzel and M. I. Freidlin,*Fluctuations in Dynamical Systems under the Action of Small Random Perturbations*, ``Nauka'', Moscow, 1979; English transl., Springer Verlag, Berlin, 1984.**4.**I. Gikhman and A. V. Skorokhod,*Stochastic Differential Equations*, ``Naukova Dumka'', Kiev, 1968; English transl., Springer Verlag, Berlin, 1972.**5.**R. Sh. Liptser and P. Chiganskiĭ,*Moderate deviations for a diffusion-type process in a random environment*, Teor. Veroyatn. Primen.**54**(2009), no. 1, 39–62 (Russian, with Russian summary); English transl., Theory Probab. Appl.**54**(2010), no. 1, 29–50. MR**2766646**, 10.1137/S0040585X97983973**6.**A. A. Pukhalskiĭ,*Large Deviations of Stochastic Dynamical Systems*, ``Fizmatlit'', Moscow, 2005. (Russian)**7.**A. D. Wentzell,*Limit theorems on large deviations for Markov stochastic processes*, Mathematics and its Applications (Soviet Series), vol. 38, Kluwer Academic Publishers Group, Dordrecht, 1990. Translated from the Russian. MR**1135113****8.**Ī. V. Samoĭlenko,*Large deviations for random evolutions with independent increments in the scheme of Poisson approximation*, Teor. Ĭmovīr. Mat. Stat.**85**(2011), 95–101 (Ukrainian, with English, Russian and Ukrainian summaries); English transl., Theory Probab. Math. Statist.**85**(2012), 107–114. MR**2933707**, 10.1090/S0094-9000-2013-00878-3**9.**D. S. Budkov and S. Ya. Makhno,*The law of the iterated logarithm for solutions of stochastic equations*, Teor. Ĭmovīr. Mat. Stat.**83**(2010), 39–48 (Russian, with English and Russian summaries); English transl., Theory Probab. Math. Statist.**83**(2011), 47–57. MR**2768847**, 10.1090/S0094-9000-2012-00840-5

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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