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The Extended Large Deviation Principle for the Trajectories of a Compound Renewal Process
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Journal Article
The Extended Large Deviation Principle for the Trajectories of a Compound Renewal Process
2022
Overview
We study a homogeneous compound renewal process (c.r.p.)
. It is assumed that the elements of the sequence that rules the process satisfy Cramér’s moment condition
. We consider the family of processes
where
as
. Conditions are proposed under which the extended large deviation principle holds for the trajectories
in the space
of functions with bounded variation, endowed with Borovkov’s metric. If the trajectories of the process
are monotone with probability 1 then, under the same condition, we prove the classical trajectory large deviation principle.
Publisher
Pleiades Publishing,Springer Nature B.V
Subject
