On the tails of Dickman-like perpetuities

TL;DR

This paper analyzes the tail behavior of certain perpetuities with distributions similar to the Dickman distribution using a probabilistic exponential change of measure technique.

Contribution

It provides a precise tail asymptotic analysis for perpetuities with distributions close to the Dickman distribution, employing a novel probabilistic approach.

Findings

Derived exact tail asymptotics for Dickman-like perpetuities

Introduced a probabilistic method based on exponential change of measure

Enhanced understanding of tail behavior in related stochastic models

Abstract

By using a probabilistic technique based on the exponential change of measure we find a precise tail asymptotic behavior of some perpetuities with distributions close to the Dickman distribution.