Antonia Földes

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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 [19] 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)
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)