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 Mat. Tr., 2013, Volume 16, Number 2, Pages 45–68 (Mi mt259)

Conditional moderately large deviation principles for the trajectories of random walks and processes with independent increments

A. A. Borovkovab, A. A. Mogul'skiĭab

a Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences, Novosibirsk, Russia
b Novosibirsk State University, Novosibirsk, Russia

Abstract: We extend the large deviation principles for random walks and processes with independent increments to the case of conditional probabilities given that the position of the trajectory at the last time moment is localized in a neighborhood of some point. As a corollary, we obtain a moderately large deviation principle for empirical distributions (an analog of Sanov's theorem).

Key words: moderately large deviation principle, local moderately large deviation principle, conditional moderately large deviation principle.

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English version:
Siberian Advances in Mathematics, 2015, 25:1, 39–55

Bibliographic databases:

UDC: 519.21

Citation: A. A. Borovkov, A. A. Mogul'skiǐ, “Conditional moderately large deviation principles for the trajectories of random walks and processes with independent increments”, Mat. Tr., 16:2 (2013), 45–68; Siberian Adv. Math., 25:1 (2015), 39–55

Citation in format AMSBIB
\Bibitem{BorMog13} \by A.~A.~Borovkov, A.~A.~Mogul'ski{\v\i} \paper Conditional moderately large deviation principles for the trajectories of random walks and processes with independent increments \jour Mat. Tr. \yr 2013 \vol 16 \issue 2 \pages 45--68 \mathnet{http://mi.mathnet.ru/mt259} \mathscinet{http://www.ams.org/mathscinet-getitem?mr=3184037} \transl \jour Siberian Adv. Math. \yr 2015 \vol 25 \issue 1 \pages 39--55 \crossref{https://doi.org/10.3103/S1055134415010058}