Logarithmic averages for the local times of recurrent random walks and Levy processes
نویسندگان
چکیده
منابع مشابه
On 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...
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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...
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We prove that when a sequence of Lévy processes X(n) or a normed sequence of random walks S(n) converges a.s. on the Skorokhod space toward a Lévy process X, the sequence L(n) of local times at the supremum of X(n) converges uniformly on compact sets in probability toward the local time at the supremum of X. A consequence of this result is that the sequence of (quadrivariate) ladder processes (...
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ژورنال
عنوان ژورنال: Stochastic Processes and their Applications
سال: 1995
ISSN: 0304-4149
DOI: 10.1016/0304-4149(95)00045-9