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Journals and Conferences
This paper is devoted to the study of the additive functional t → ∫ t 0 f(W (s))ds, where f denotes a measurable function and W is a planar Brownian motion. Kasahara and Kotani  have obtained its second-order asymptotic behaviors, by using the skewproduct representation of W and the ergodicity of the angular part. We prove that the vector ( ∫ · 0 fj(W… (More)
It is well known that, asymptotically, the appropriately normalized uniform Vervaat process, i.e., the integrated uniform Bahadur–Kiefer process properly normalized, behaves like the square of the uniform empirical process. We give a complete description of the strong and weak asymptotic behaviour in sup-norm of this representation of the Vervaat process… (More)
Sample path properties of a class of additive functionals of two-dimensional Brownian motion and random walk are studied. AMS 1991 Subject Classification: Primary 60J15; Secondary 60F15, 60J55.
We prove strong invariance principle between a transient Bessel process and a certain nearest neighbor (NN) random walk that is constructed from the former by using stopping times. We show that their local times are close enough to share the same strong limit theorems. It is also shown, that if the di erence between the distributions of two NN random walks… (More)
We study the occupation measure of various sets for a symmetric transient random walk in Z with finite variances. Let mn ðAÞ denote the occupation time of the set A up to time n. It is shown that supx2Zd m X n ðx þ AÞ= log n tends to a finite limit as n ! 1. The limit is expressed in terms of the largest eigenvalue of a matrix involving the Green function… (More)
For a simple symmetric random walk in dimension d ≥ 3, a uniform strong law of large numbers is proved for the number of sites with given local time up to time n. AMS 2000 Subject Classification: Primary 60G50; Secondary 60F15, 60J55.