Large deviations asymptotics for large waiting times

TL;DR

This paper analyzes the probabilities of unusually large waiting times in Bernoulli processes, deriving explicit rate functions and establishing a large deviation principle with a novel rate function not derived from a free energy transform.

Contribution

It provides explicit rate functions and proves a large deviations principle for large waiting times in Bernoulli processes, highlighting a new type of rate function.

Findings

Explicit rate functions for large waiting times

Large deviation principle established without Legendre transform

Novel rate function not derived from free energy

Abstract

In this paper we investigate the statistics of large waiting times (with respect to the total waiting time) for Bernoulli processes. We determine the corresponding rate functions explicitly and prove a large deviations asymptotic. By this we have estabished a large deviation principle for which the rate function is not the Legendre transform of some free energy function.