Limit laws for functionals of self-intersection symmetric alpha-stable processes

TL;DR

This paper establishes limit laws for functionals of self-intersection symmetric alpha-stable processes with alpha between 1 and 2, using advanced probabilistic methods like moments, sample configuration, and chaining.

Contribution

It introduces new limit laws for self-intersection functionals of alpha-stable processes, extending existing theories with novel methodological approaches.

Findings

Proves two limit laws for self-intersection functionals

Employs method of moments and chaining techniques

Extends understanding of alpha-stable process behaviors

Abstract

In this paper, we prove two limit laws for functionals of self-intersection symmetric alpha-stable processes with alpha\in(1,2). The results are obtained based on the method of moments, the sample configuration and the chaining argument introduced in (Nualart and Xu 2013) are employed.