A. A. Borovkov, A. A. Mogul'skiǐ, “On large deviation principles in metric spaces”, Sibirsk. Mat. Zh., 51:6 (2010), 1251–1269; Siberian Math. J., 51:6 (2010), 989

Sibirskii Matematicheskii Zhurnal

RUS ENG

JOURNALS PEOPLE ORGANISATIONS CONFERENCES SEMINARS VIDEO LIBRARY PACKAGE AMSBIB

JavaScript is disabled in your browser. Please switch it on to enable full functionality of the website

	General information
	Latest issue
	Archive
	Impact factor

	Search papers
	Search references

	RSS
	Latest issue
	Current issues
	Archive issues
	What is RSS

Sibirsk. Mat. Zh.:
Year:
Volume:
Issue:
Page:
	Find

Personal entry:
Login:
Password:
	Save password
	Enter
	Forgotten password?
	Register

Sibirskii Matematicheskii Zhurnal, 2010, Volume 51, Number 6, Pages 1251–1269 (Mi smj2159)

This article is cited in 29 scientific papers (total in 29 papers)

On large deviation principles in metric spaces

A. A. Borovkov^ab, A. A. Mogul'skiĭ^ab

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

Full-text PDF (384 kB) Citations (29)

References:

PDF

HTML

Abstract: Many articles deal with large deviation principles (LDPs) (see [1–4] for instance and the references in [3, 4]), studying mainly the LDP for the sums of random elements or for various stochastic models and dynamical systems. For a sequence of random elements in a metric space, in studying LDPs it turns out natural to introduce the concepts of the local LDP and extended LDP. They enable us to state and prove LDP-type statements in those cases when the usual LDP (cf. [3, 4]) fails (see [5, 6] and Section 6 of this article). We obtain conditions for the fulfillment of the extended LDP in metric spaces. The main among these conditions is the fulfillment of the local LDP. The latter is usually much simpler to prove than the extended LDP.

Keywords: large deviation principle, extended large deviation principle, local large deviation principle, deviation function, totally bounded set, compact set.

Received: 01.02.2010

English version:
Siberian Mathematical Journal, 2010, Volume 51, Issue 6, Pages 989–1003
DOI: https://doi.org/10.1007/s11202-010-0098-0

Bibliographic databases:

Document Type: Article

UDC: 519.21

Language: Russian

Citation: A. A. Borovkov, A. A. Mogul'skiǐ, “On large deviation principles in metric spaces”, Sibirsk. Mat. Zh., 51:6 (2010), 1251–1269; Siberian Math. J., 51:6 (2010), 989–1003

Citation in format AMSBIB

\Bibitem{BorMog10}

\by A.~A.~Borovkov, A.~A.~Mogul'ski{\v\i}

\paper On large deviation principles in metric spaces

\jour Sibirsk. Mat. Zh.

\yr 2010

\vol 51

\issue 6

\pages 1251--1269

\mathnet{http://mi.mathnet.ru/smj2159}

\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=2797595}

\elib{https://elibrary.ru/item.asp?id=15563606}

\transl

\jour Siberian Math. J.

\yr 2010

\vol 51

\issue 6

\pages 989--1003

\crossref{https://doi.org/10.1007/s11202-010-0098-0}

\isi{https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=Publons&SrcAuth=Publons_CEL&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=000288180800005}

\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-78650729115}

Linking options:

https://www.mathnet.ru/eng/smj2159

https://www.mathnet.ru/eng/smj/v51/i6/p1251

This publication is cited in the following 29 articles:

Mihail Bazhba, Chang-Han Rhee, Bert Zwart, “Large deviations for stochastic fluid networks with Weibullian tails”, Queueing Syst, 102:1-2 (2022), 25
A. A. Mogul'skiǐ, “The Extended Large Deviation Principle for the Trajectories of a Compound Renewal Process”, Sib. Adv. Math., 32:1 (2022), 35
A. A. Mogulskii, “Rasshirennyi printsip bolshikh uklonenii dlya traektorii obobschennogo protsessa vosstanovleniya”, Matem. tr., 24:1 (2021), 142–174
Logachov A. Logachova O. Yambartsev A., “The Local Principle of Large Deviations For Compound Poisson Process With Catastrophes”, Braz. J. Probab. Stat., 35:2 (2021), 205–223
Vysotsky V., “Contraction Principle For Trajectories of Random Walks and Cramer'S Theorem For Kernel-Weighted Sums”, ALEA-Latin Am. J. Probab. Math. Stat., 18:2 (2021), 1103–1125
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
Sharov K.S., “Creating and Applying Sir Modified Compartmental Model For Calculation of Covid-19 Lockdown Efficiency”, Chaos Solitons Fractals, 141 (2020), 110295
Bazhba M., Blanchet J., Rhee Ch.-H., Zwart B., “Sample Path Large Deviations For Levy Processes and Random Walks With Weibull Increments”, Ann. Appl. Probab., 30:6 (2020), 2695–2739
Logachov A., Logachova O., Yambartsev A., “Local Large Deviation Principle For Wiener Process With Random Resetting”, Stoch. Dyn., 20:5 (2020), 2050032
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
Bakhtin V.I., Lebedev A.V., “Entropy Statistic Theorem and Variational Principle For T-Entropy Are Equivalent”, J. Math. Anal. Appl., 474:1 (2019), 59–71
N. D. Vvedenskaya, A. V. Logachov, Yu. M. Suhov, A. A. Yambartsev, “A local large deviation principle for inhomogeneous birth-death processes”, Problems Inform. Transmission, 54:3 (2018), 263–280
A. A. Mogul'skiǐ, “The extended large deviation principle for a process with independent increments”, Siberian Math. J., 58:3 (2017), 515–524
A. A. Mogul'skiǐ, “The large deviation principle for a compound Poisson process”, Siberian Adv. Math., 27:3 (2017), 160–186
Bakhtin V., Sokal E., “the Kullback-Leibler Information Function For Infinite Measures”, Entropy, 18:12 (2016), 448
Huang G., Mandjes M., Spreij P., “Large Deviations For Markov-Modulated Diffusion Processes With Rapid Switching”, Stoch. Process. Their Appl., 126:6 (2016), 1785–1818
Artem V. Logachov, “The local principle of large deviations for solutions of Itô stochastic equations with quick drift”, J Math Sci, 218:1 (2016), 28
Klebaner F.C., Logachov A.V., Mogulskii A.A., “Large Deviations For Processes on Half-Line”, Electron. Commun. Probab., 20 (2015), 75, 1–14
V. I. Bakhtin, “Spektralnyi potentsial, deistvie Kulbaka i printsip bolshikh uklonenii dlya konechno-additivnykh mer”, Tr. In-ta matem., 23:2 (2015), 11–23
A. A. Borovkov, A. A. Mogul'skiǐ, “Large deviation principles for sums of random vectors and the corresponding renewal functions in the inhomogeneous case”, Siberian Adv. Math., 25:4 (2015), 255–267

Citing articles in Google Scholar: Russian citations, English citations
Related articles in Google Scholar: Russian articles, English articles

Statistics & downloads:
Abstract page:	659
Full-text PDF :	171
References:	87
First page:	3

Что такое QR-код?

Registration to the website

Logotypes