Moderate deviations and laws of the iterated logarithm for the local times of additive Lévy processes and additive random walks

Abstract

We study the upper tail behaviors of the local times of the additive Lévy processes and additive random walks. The limit forms we establish are the moderate deviations and the laws of the iterated logarithm for the L₂-norms of the local times and for the local times at a fixed site.