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.
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页码：35 / 57
页数：22
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