Moderate deviations and laws of the iterated logarithm for the local times of additive L\'{e}vy processes and additive random walks

TL;DR

This paper investigates the probabilistic behavior of local times in additive Lévy processes and random walks, establishing moderate deviation principles and laws of the iterated logarithm for their L2-norms and fixed-site local times.

Contribution

It introduces new limit theorems for the tail behavior of local times in additive Lévy processes and random walks, expanding understanding of their asymptotic properties.

Findings

Established moderate deviation principles for local times.

Proved laws of the iterated logarithm for local times.

Analyzed the asymptotic behavior of local times at fixed sites.

Abstract

We study the upper tail behaviors of the local times of the additive L\'{e}vy processes and additive random walks. The limit forms we establish are the moderate deviations and the laws of the iterated logarithm for the L_2-norms of the local times and for the local times at a fixed site.