Integro-Local Theorems in Boundary Crossing Problems for Compound Renewal Processes

Аннотация

We find sharp asymptotics for the probability that the moment when the trajectory of a compound renewal process crosses an arbitrary remote boundary lies in a prescribed small time interval. As a key step in our proof, we obtain limit theorems for the conditional distribution of jumps of the process when the endpoint of the trajectory of a compound renewal process is fixed.