@article{e3d61afbcc7b467280f582824e72080c,
title = "A remark on normalizations in a local large deviations principle for inhomogeneous birth-and-death process",
abstract = "This work is a continuation of [13].We consider a continuoustime 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, large deviations principle, local large deviations principle, normalization (scaling), rate function",
author = "Logachov, {A. V.} and Suhov, {Y. M.} and Vvedenskaya, {N. D.} and Yambartsev, {A. A.}",
note = "Funding Information: NDV thanks Russian Science Foundation for the financial support through Grant 14-50-00150. AVL thanks FAPESP (S ao 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 {\~a}., published September, 7, 2020.",
year = "2020",
doi = "10.33048/semi.2020.17.092",
language = "English",
volume = "17",
pages = "1258--1269",
journal = "Сибирские электронные математические известия",
issn = "1813-3304",
publisher = "Sobolev Institute of Mathematics",
}