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Teor. Veroyatnost. i Primenen., 2013, Volume 58, Issue 1, Pages 37–52 (Mi tvp4493)  

This article is cited in 12 scientific papers (total in 12 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

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.

DOI: https://doi.org/10.4213/tvp4493

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English version:
Theory of Probability and its Applications, 2014, 58:1, 25–37

Bibliographic databases:

MSC: 60F10, 60G50
Received: 02.08.2011
Revised: 14.06.2012

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 articles:
    1. A. A. Borovkov, A. A. Mogul'skiǐ, “Conditional moderately large deviation principles for the trajectories of random walks and processes with independent increments”, Siberian Adv. Math., 25:1 (2015), 39–55  mathnet  crossref  mathscinet
    2. A. A. Borovkov, A. A. Mogul'skii, “Moderately large deviation principles for trajectories of random walks and processes with independent increments”, Theory Probab. Appl., 58:4 (2014), 562–581  mathnet  crossref  crossref  mathscinet  isi  elib  elib
    3. A. A. Borovkov, A. A. Mogul'skiǐ, “Large deviation principles for the finite-dimensional distributions of compound renewal processes”, Siberian Math. J., 56:1 (2015), 28–53  mathnet  crossref  mathscinet  isi  elib  elib
    4. A. A. Borovkov, A. A. Mogul'skii, “Large deviation principles for trajectories of compound renewal processes. I”, Theory Probab. Appl., 60:2 (2016), 207–221  mathnet  crossref  crossref  mathscinet  isi  elib
    5. A. A. Mogul'skiǐ, “The large deviation principle for a compound Poisson process”, Siberian Adv. Math., 27:3 (2017), 160–186  mathnet  crossref  crossref  elib
    6. Bakhtin V. Sokal E., “The Kullback–Leibler Information Function for Infinite Measures”, Entropy, 18:12 (2016), 448  crossref  isi  elib  scopus
    7. A. A. Mogul'skiǐ, “The extended large deviation principle for a process with independent increments”, Siberian Math. J., 58:3 (2017), 515–524  mathnet  crossref  crossref  isi  elib  elib
    8. A. A. Borovkov, “Functional limit theorems for compound renewal processes”, Siberian Math. J., 60:1 (2019), 27–40  mathnet  crossref  crossref  mathscinet  isi  elib
    9. F. C. Klebaner, A. A. Mogulskii, “Large deviations for processes on half-line: Random Walk and Compound Poisson Process”, Sib. elektron. matem. izv., 16 (2019), 1–20  mathnet  crossref
    10. F. C. Klebaner, A. V. Logachov, A. A. Mogulskii, “Extended large deviation principle for trajectories of processes with independent and stationary increments on the half-line”, Problems Inform. Transmission, 56:1 (2020), 56–72  mathnet  crossref  crossref  isi  elib
    11. A. A. Borovkov, “O tochnykh printsipakh bolshikh uklonenii dlya obobschennogo protsessa vosstanovleniya”, Teoriya veroyatn. i ee primen., 66:2 (2021), 214–230  mathnet  crossref
    12. A. A. Mogulskii, “Rasshirennyi printsip bolshikh uklonenii dlya traektorii obobschennogo protsessa vosstanovleniya”, Matem. tr., 24:1 (2021), 142–174  mathnet  crossref
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