We study the object formally defined as where Xt denotes the symmetric stable processes of index 0[beta]=2 in Rd. When , this has to be defined as a limit, in the spirit of renormalized self-intersection local time. We obtain results about the large deviations and laws of the iterated logarithm...

In this paper, we establish the moderate deviations for occupation times of Markov processes under the conditions given in Darling-Kac (1957. Trans. Amer. Math. Soc. 84, 444-458). When applied to the law of the iterated logarithm, our results generalize those obtained in Marcus-Rosen (1994a....

Let {Xn}n[greater-or-equal, slanted]0 be a Harris recurrent Markov chain with state space E and let [xi] be a measurable map from E to a separable Banach space B and setSome integrabilities and tail behaviors of Sn over one excursion between two visits to a subset A of E are considered. It is...

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 X1(t),...,Xp(t) be independent, d-dimensional symmetric stable processes with...