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

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