Laws of the Iterated Logarithm for the Local Times of Symmetric Levy Processes and Recurrent Random Walks
نویسندگان
چکیده
منابع مشابه
Functional laws of the iterated logarithm for local times of recurrent random walks on Z2
We prove functional laws of the iterated logarithm for L~, the number of returns to the origin, up to step n, of recurrent random walks on Z~ with slowly varying partial Green’s function. We find two distinct functional laws of the iterated logarithm depending on the scaling used. In the special case of finite variance random walks, we obtain one limit set for 0 ~ 1, and a different limit set f...
متن کاملModerate Deviations and Laws of the Iterated Logarithm for the Local times of Additive Lévy Processes and Additive Random Walks
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. Subject classifications: 60F10, 60F15, 60J55, 60G52
متن کاملOn the Law of the Iterated Logarithm for Local Times of Recurrent Random Walks
We consider the law of the iterated logarithm (LIL) for the local time of one-dimensional recurrent random walks. First we show that the constants in the LIL for the local time and for its supremum (with respect to the space variable) are equal under a very general condition given in Jain and Pruitt (1984). Second we evaluate the common value of the constants, as the random walk is in the domai...
متن کاملModerate deviations and laws of the iterated logarithm for the renormalized self-intersection local times of planar random walks
We study moderate deviations for the renormalized self-intersection local time of planar random walks. We also prove laws of the iterated logarithm for such local times
متن کاملLaws of the Iterated Logarithm for Symmetric Jump Processes
Based on two-sided heat kernel estimates for a class of symmetric jump processes on metric measure spaces, the laws of the iterated logarithm (LILs) for sample paths, local times and ranges are established. In particular, the LILs are obtained for β-stable-like processes on α-sets with β > 0.
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ژورنال
عنوان ژورنال: The Annals of Probability
سال: 1994
ISSN: 0091-1798
DOI: 10.1214/aop/1176988723