A large-deviation principle for birth-death processes with a linear rate of downward jumps

被引：1

作者：

Logachov, Artem ^{[1
,2
,3
]}

Suhov, Yuri ^{[4
]}

Vvedenskaya, Nikita ^{[5
]}

Yambartsev, Anatoly ^{[6
]}

机构：

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

[2] Novosibirsk State Tech Univ, Pr K Marksa 20, Novosibirsk 630073, Russia

[3] Sobolev Inst Math, 4 Koptyugaave, Novosibirsk 630090, Russia

[4] Penn State Univ, Dept Math, State Coll, PA 16802 USA

[5] RAS, Kharkevich Inst Informat Transmiss Problems, Bolshoy Karetnyi Per 19, Moscow 127051, Russia

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

来源：

JOURNAL OF APPLIED PROBABILITY | 2024年 / 61卷 / 03期

关键词：

Large-deviation principle; local large-deviation principle; birth-death processes; rate functional; INHOMOGENEOUS BIRTH;

D O I：

10.1017/jpr.2023.75

中图分类号：

O21 [概率论与数理统计]; C8 [统计学];

学科分类号：

020208 ; 070103 ; 0714 ;

摘要：

Birth-death processes form a natural class where ideas and results on large deviations can be tested. We derive a large-deviation principle under an assumption that the rate of jump down (death) grows asymptotically linearly with the population size, while the rate of jump up (birth) grows sublinearly. We establish a large-deviation principle under various forms of scaling of the underlying process and the corresponding normalization of the logarithm of the large-deviation probabilities. The results show interesting features of dependence of the rate functional upon the parameters of the process and the forms of scaling and normalization.

引用

页码：781 / 801

页数：21

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