Local asymptotic self-similarity for heavy tailed harmonizable fractional L\'evy motions

TL;DR

This paper investigates the local asymptotic self-similarity of harmonizable fractional Lévy motions with heavy tails, showing the tangent process is a harmonizable fractional stable motion and providing conditions for their existence.

Contribution

It characterizes the local asymptotic self-similarity of heavy-tailed harmonizable fractional Lévy motions and identifies the tangent process as a stable motion, along with existence conditions.

Findings

Tangent process is harmonizable fractional stable motion.

Provides sufficient conditions for existence.

Characterizes local asymptotic self-similarity.

Abstract

In this work we characterize the local asymptotic self-similarity of harmonizable fractional L\'evy motions in the heavy tailed case. The corresponding tangent process is shown to be the harmonizable fractional stable motion. In addition, we provide sufficient conditions for existence of harmonizable fractional L\'evy motions.