Functional limit theorems for Levy processes and their almost-sure versions

TL;DR

This paper establishes a convergence criterion in Skorokhod space and applies it to Levy processes to derive almost-sure limit theorems, advancing understanding of their probabilistic behavior.

Contribution

Introduces a new convergence criterion in Skorokhod space and derives almost-sure limit theorems for specific Levy processes using this criterion.

Findings

Established a new convergence criterion in Skorokhod space

Derived almost-sure limit theorems for Levy processes

Enhanced understanding of Levy process convergence behaviors

Abstract

In this paper we prove a criterion of convergence in distribution in Skorokhod space. We apply this criterion to some special Levy processes and obtain almost-sure versions of limit theorems for these processes.