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MODERATE DEVIATIONS AND LAWS OF THE ITERATED LOGARITHM FOR THE LOCAL TIMES OF ADDITIVE LÉVY PROCESSES AND ADDITIVE RANDOM WALKS

By Xia Chen

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. 1. Introduction. Let X(t) be a d-dimensional symmetric Lévy process with the characteristic exponent ψ(λ), that is, Ee iλ·X(t) = e −tψ(λ) , t ≥ 0, λ ∈ R d. The symmetry assumption implies that ψ(λ) takes only real values and ψ(λ) ≥ 0. Throughout we assume that there is a deterministic and positiv

Year: 2007
DOI identifier: 10.1214/009117906000000520
OAI identifier: oai:CiteSeerX.psu:10.1.1.249.6656
Provided by: CiteSeerX
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