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Sibirskie Èlektronnye Matematicheskie Izvestiya [Siberian Electronic Mathematical Reports], 2020, Volume 17, Pages 1258–1269
DOI: https://doi.org/10.33048/semi.2020.17.092 (Mi semr1286) 		 
This article is cited in 1 scientific paper (total in 1 paper)

Probability theory and mathematical statistics

A remark on normalizations in a local large deviations principle for inhomogeneous birth – and – death process

A. V. Logachovabcd, Y. M. Suhovef, N. D. Vvedenskayag, A. A. Yambartsevh

a Lab. of Probability Theory and Math. Statistics, Sobolev Institute of Mathematics, 4, Koptyuga ave., Novosibirsk, 630090, Russia
b Novosibirsk State University, 1, Pirogova str. Novosibirsk, 630090, Russia
c Dep. of High Math., Siberian State University of Geosystems and Technologies, 10, Plahotnogo str., Novosibirsk, 630108, Russia
d Novosibirsk State University of Economics and Management, 56, Kamenskaya str., Novosibirsk, 630099, Russia
e Math. Department, Penn State University, McAllister Buid, University Park, State College, PA 16802, USA
f Statistical Laboratory, DPMMS, University of Cambridge, Wilberforce Rd, Cambridge CB3 0WB, United Kingdom
g Institute for Information Transmission Problems, RAS, 19, Bolshoj Karetnyj Per., Moscow, 127051, Russia
h Institute of Mathematics and Statistics, University of São Paulo, Rua do Matão 1010, CEP 05508-090, São Paulo SP, Brazil
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DOI: https://doi.org/10.33048/semi.2020.17.092
Abstract: This work is a continuation of [13]. We consider a continuous-time birth – and – death process in which the transition rates are regularly varying function of the process position. We establish rough exponential asymptotic for the probability that a sample path of a normalized process lies in a neighborhood of a given nonnegative continuous function. We propose a variety of normalization schemes for which the large deviation functional preserves its natural integral form.
Keywords: birth – and – death process, normalization (scaling), large deviations principle, local large deviations principle, rate function.
Funding agency Grant number
Russian Science Foundation 14-50-00150
Fundação de Amparo à Pesquisa do Estado de São Paulo 2017/20482
2017/10555-0
Russian Foundation for Basic Research 18-01-00101_а
National Council for Scientific and Technological Development (CNPq) 301050/2016-3
NDV thanks Russian Science Foundation for the financial support through Grant 14-50-00150. AVL thanks FAPESP (São Paulo Research Foundation) for the financial support via Grant 2017/20482 and also thanks RFBR (Russian Foundation for Basic Research) grant 18-01-00101. YMS thanks The Math Department, Penn State University, for hospitality and support and St John's College, Cambridge, for financial support. AAY thanks CNPq (National Council for Scientific and Technological Development) and FAPESP for the financial support via Grants 301050/2016-3 and 2017/10555-0, respectively.
Received November 11, 2019, published September 7, 2020
Bibliographic databases:
Document Type: Article
UDC: 519.21
MSC: 60F10
Language: English
Citation: A. V. Logachov, Y. M. Suhov, N. D. Vvedenskaya, A. A. Yambartsev, “A remark on normalizations in a local large deviations principle for inhomogeneous birth – and – death process”, Sib. Èlektron. Mat. Izv., 17 (2020), 1258–1269
Citation in format AMSBIB
\Bibitem{LogSukVve20}
\by A.~V.~Logachov, Y.~M.~Suhov, N.~D.~Vvedenskaya, A.~A.~Yambartsev
\paper A remark on normalizations in a local large deviations principle for inhomogeneous birth -- and -- death process
\jour Sib. \`Elektron. Mat. Izv.
\yr 2020
\vol 17
\pages 1258--1269
\mathnet{http://mi.mathnet.ru/semr1286}
\crossref{https://doi.org/10.33048/semi.2020.17.092}
\isi{https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=Publons&SrcAuth=Publons_CEL&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=000567361200001}
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