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Perturbed and non-perturbed Brownian taboo processes. (English) Zbl 0989.60076
Summary: We study the Brownian taboo process, which is a version of Brownian motion conditioned to stay within a finite interval, and the \(\alpha\)-perturbed Brownian taboo process, which is an analogous version of an \(\alpha\)-perturbed Brownian motion. We are particularly interested in the asymptotic behaviour of the supremum of the taboo process, and our main results give integral tests for upper and lower functions of the supremum as \(t\to\infty\). In the Brownian case these include extensions of recent results by A. Lambert [ibid. 36, No. 2, 251-274 (2000; Zbl 0970.60055)], but are proved in a quite different way.
60J65 Brownian motion
60K05 Renewal theory
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