A REMARK ON NORMALIZATIONS IN A LOCAL LARGE DEVIATIONS PRINCIPLE FOR INHOMOGENEOUS BIRTH - AND - DEATH PROCESS

被引：5

作者：

Logachov, A., V ^{[1
,2
,3
,4
]}

Suhov, Y. M. ^{[5
,6
]}

Vvedenskaya, N. D. ^{[7
]}

Yambartsev, A. A. ^{[8
]}

机构：

[1] Sobolev Inst Math, Lab Probabil Theory & Math Stat, 4 Koptyuga Ave, Novosibirsk 630090, Russia

[2] Novosibirsk State Univ, 1 Pirogova Str, Novosibirsk 630090, Russia

[3] Siberian State Univ Geosyst & Technol, Dep High Math, 10 Plahotnogo Str, Novosibirsk 630108, Russia

[4] Novosibirsk State Univ Econ & Management, 56 Kamenskaya Str, Novosibirsk 630099, Russia

[5] Penn State Univ, Dept Math, McAllister Buid, State Coll, PA 16802 USA

[6] Univ Cambridge, Stat Lab, DPMMS, Wilberforce Rd, Cambridge CB3 0WB, England

[7] RAS, Inst Informat Transmiss Problems, 19 Bolshoj Karetnyj Per, Moscow 127051, Russia

[8] Univ Sao Paulo, Inst Math & Stat, Rua Matao 1010, BR-05508090 Sao Paulo, SP, Brazil

来源：

SIBERIAN ELECTRONIC MATHEMATICAL REPORTS-SIBIRSKIE ELEKTRONNYE MATEMATICHESKIE IZVESTIYA | 2020年 / 17卷

基金：

巴西圣保罗研究基金会; 俄罗斯科学基金会; 俄罗斯基础研究基金会;

关键词：

birth - and - death process; normalization (scaling); large deviations principle; local large deviations principle; rate function;

D O I：

10.33048/semi.2020.17.092

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

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.

引用

页码：1258 / 1269

页数：12

共 15 条

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