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

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.