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Teoriya Veroyatnostei i ee Primeneniya, 2013, Volume 58, Issue 1, Pages 37–52
DOI: https://doi.org/10.4213/tvp4493 (Mi tvp4493) 		 
This article is cited in 19 scientific papers (total in 19 papers)

Large deviation principles for random walk trajectories. III

A. A. Borovkov, A. A. Mogulskii

Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences, Novosibirsk
Full-text PDF (202 kB) Citations (19)
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DOI: https://doi.org/10.4213/tvp4493
Abstract: The present paper is a continuation of [A. A. Borovkov and A. A. Mogulskii, Theory Probab. Appl. 57, No. 1, 1–27 (2013); translation from Teor. Veroyatn. Primen. 57, No. 1, 3–34 (2012; Zbl 1279.60037)]. It consists of two sections. Section 6 presents results similar to those obtained in Sections 4 and 5, but now in the space of functions of bounded variation with metric stronger than that of $\mathbb{D}$. In Section 7 we obtain the so-called conditional large deviation principles for the trajectories of univariate random walks with a localized terminal value of the walk. As a consequence, we prove a version of Sanov’s theorem on large deviations of empirical distributions.
Keywords: extended large deviation principle in the space of functions of bounded variation; local large deviation principle; integro-local Gnedenko and Stone-Shepp theorems; Sanov theorem; large deviations of empirical distributions.
Received: 02.08.2011
Revised: 14.06.2012
English version:
Theory of Probability and its Applications, 2014, Volume 58, Issue 1, Pages 25–37
DOI: https://doi.org/10.1137/S0040585X97986370
Bibliographic databases:
Document Type: Article
MSC: 60F10, 60G50
Language: Russian
Citation: A. A. Borovkov, A. A. Mogulskii, “Large deviation principles for random walk trajectories. III”, Teor. Veroyatnost. i Primenen., 58:1 (2013), 37–52; Theory Probab. Appl., 58:1 (2014), 25–37
Citation in format AMSBIB
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    This publication is cited in the following 19 articles:
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    		Теория вероятностей и ее применения Theory of Probability and its Applications
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