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

[21] Large Deviation Principles for the Processes Admitting Embedded Compound Renewal Processes
Logachov, A., V
Mogulskii, A. A.
SIBERIAN MATHEMATICAL JOURNAL, 2022, 63 (01) : 119 - 137
[22] THE MODERATE DEVIATIONS PRINCIPLE FOR THE TRAJECTORIES OF COMPOUND RENEWAL PROCESSES ON THE HALF-LINE
Logachov, A., V
Mogulskii, A. A.
SIBERIAN ELECTRONIC MATHEMATICAL REPORTS-SIBIRSKIE ELEKTRONNYE MATEMATICHESKIE IZVESTIYA, 2021, 18 (02): : 1189 - 1200
[23] A Large Deviation Principle for the Risk Process with Varying Premium
HE Xiaoxia1
2. School of Mathematics and Information Sciences
WuhanUniversityJournalofNaturalSciences, 2007, (03) : 412 - 416
[24] ON THE LARGE DEVIATION PRINCIPLE FOR A QUADRATIC FUNCTIONAL OF THE AUTOREGRESSIVE PROCESS
BRYC, W
SMOLENSKI, W
STATISTICS & PROBABILITY LETTERS, 1993, 17 (04) : 281 - 285
[25] LARGE DEVIATION PRINCIPLE FOR INTEGRAL FUNCTIONALS OF A MARKOV PROCESS
Logachov, Artem Vasil'evich
Prokopenko, Evgeny Igorevich
SIBERIAN ELECTRONIC MATHEMATICAL REPORTS-SIBIRSKIE ELEKTRONNYE MATEMATICHESKIE IZVESTIYA, 2015, 12 : 639 - 650
[26] 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
[27] Large deviation principles for the finite-dimensional distributions of compound renewal processes
A. A. Borovkov
A. A. Mogul’skiĭ
Siberian Mathematical Journal, 2015, 56 : 28 - 53
[28] Large deviation principles for the finite-dimensional distributions of compound renewal processes
Borovkov, A. A.
Mogul'skii, A. A.
SIBERIAN MATHEMATICAL JOURNAL, 2015, 56 (01) : 28 - 53
[29] The large deviation principle for the on-off Weibull sojourn process
Duffy, Ken R.
Sapozhnikov, Artem
JOURNAL OF APPLIED PROBABILITY, 2008, 45 (01) : 107 - 117
[30] Large deviation principle for a mixed fractional and jump diffusion process
Diatta, Raphael
Manga, Clement
Diedhiou, Alassane
RANDOM OPERATORS AND STOCHASTIC EQUATIONS, 2022, 30 (04) : 241 - 249

← 1 2 3 4 5 →