Orderly divergence of Levy Gamma integrals

TL;DR

This paper investigates the limit behavior of weighted stochastic Gamma integrals, revealing new phenomena when functions are non-monotonic, extending classical limit theorems in probability theory.

Contribution

It introduces the concept of 'orderly divergence' for Gamma integrals and explores its implications beyond traditional monotonic function cases.

Findings

Identifies conditions for limit theorems in non-monotonic cases

Shows differences between continuous Gamma integrals and discrete sums

Highlights new aspects in divergence behavior

Abstract

``Orderly divergence'' deals with limit theorems for weighted stochastic Gamma integrals of otherwise nonintegrable functions. Although for monotonic functions this category usually coincides with the classical notion of weighted limit theorems for sums of i.i.d. random variables but there are exceptions and the lack of monotonicity reveals new aspects that are absent in the discrete case.