The Extended Large Deviation Principle for the Trajectories of a Compound Renewal Process

被引：0

作者：

Mogul’skiĭ A.A. ^{[1
]}

机构：

[1] Sobolev Institute of Mathematics, Novosibirsk

来源：

Siberian Advances in Mathematics | 2022年 / 32卷 / 1期

基金：

俄罗斯科学基金会;

关键词：

(first) compound renewal process; classical) large deviation principle; Cramér’s moment condition; deviation functional; deviation rate function; extended large deviation principle; large deviations;

D O I：

10.1134/S1055134422010047

中图分类号：

学科分类号：

摘要：

Abstract: We study a homogeneous compound renewal process (c.r.p.) (Formula presented.). It is assumed that the elements of the sequencethat rules the process satisfy Cramér’s moment condition (Formula presented.). We consider the family of processes $(Formula presented.) where (Formula presented.) as (Formula presented.). Conditions are proposed under which the extended large deviation principle holdsfor the trajectories (Formula presented.) in the space (Formula presented.) of functions with bounded variation, endowed withBorovkov’s metric. If the trajectories of the process (Formula presented.) are monotone with probability 1 then, underthe same condition, we prove the classical trajectory large deviation principle. © 2022, Pleiades Publishing, Ltd.

引用

页码：35 / 57

页数：22

共 50 条

[1] The large deviation principle for a compound Poisson process
Mogul’skiĭ A.A.
Siberian Advances in Mathematics, 2017, 27 (3) : 160 - 186
[2] LARGE DEVIATION PRINCIPLE FOR MULTIDIMENSIONAL FIRST COMPOUND RENEWAL PROCESSES IN THE PHASE SPACE
Mogulskii, Anatolii Alfredovich
Prokopenko, Evgenii Igorevich
SIBERIAN ELECTRONIC MATHEMATICAL REPORTS-SIBIRSKIE ELEKTRONNYE MATEMATICHESKIE IZVESTIYA, 2019, 16 : 1464 - 1477
[3] LARGE DEVIATION PRINCIPLE FOR MULTIDIMENSIONAL SECOND COMPOUND RENEWAL PROCESSES IN THE PHASE SPACE
Mogulskii, Anatolii Alfredovich
Prokopenko, Evgenii Igorevich
SIBERIAN ELECTRONIC MATHEMATICAL REPORTS-SIBIRSKIE ELEKTRONNYE MATEMATICHESKIE IZVESTIYA, 2019, 16 : 1478 - 1492
[4] LARGE DEVIATION PRINCIPLES FOR TRAJECTORIES OF COMPOUND RENEWAL PROCESSES. II
Borovkov, A. A.
Mogulskii, A. A.
THEORY OF PROBABILITY AND ITS APPLICATIONS, 2016, 60 (03) : 349 - 366
[5] The extended large deviation principle for a process with independent increments
Mogul'skii, A. A.
SIBERIAN MATHEMATICAL JOURNAL, 2017, 58 (03) : 515 - 524
[6] The extended large deviation principle for a process with independent increments
A. A. Mogul’skiĭ
Siberian Mathematical Journal, 2017, 58 : 515 - 524
[7] ON EXACT LARGE DEVIATION PRINCIPLES FOR COMPOUND RENEWAL PROCESSES
Borovkov, A. A.
THEORY OF PROBABILITY AND ITS APPLICATIONS, 2021, 66 (02) : 170 - 183
[8] Extended Large Deviation Principle for Trajectories of Processes with Independent and Stationary Increments on the Half-line
F. C. Klebaner
A. V. Logachov
A. A. Mogulskii
Problems of Information Transmission, 2020, 56 : 56 - 72
[9] Extended Large Deviation Principle for Trajectories of Processes with Independent and Stationary Increments on the Half-line
Klebaner, F. C.
Logachov, A. V.
Mogulskii, A. A.
PROBLEMS OF INFORMATION TRANSMISSION, 2020, 56 (01) : 56 - 72
[10] The Large Deviation Principle for Finite-Dimensional Distributions of Multidimensional Renewal Processes
Mogul’skiĭ A.A.
Prokopenko E.I.
Siberian Advances in Mathematics, 2021, 31 (3) : 188 - 208

← 1 2 3 4 5 →