Self-intersection local times of additive processes: Large deviation and law of the iterated logarithm

摘要

Recently, we studied the large deviations for the local times of additive stable processes. In this work, we investigate the upper tail behaviors of the self-intersection local times of additive stable processes. Let X-1 (t),..., X-p(t) be independent, d-dimensional symmetric stable processes with stable index alpha < Ce <= 2 and consider the additive stable process (X) over bar (t(1),..., t(p)) = X, (t(1)) + (...) + X-p(t(p)). Under the condition d < alpha p, we compute large deviation probabilities for the self-intersection local time