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Teor. Veroyatnost. i Primenen., 2013, Volume 58, Issue 2, Pages 381–387 (Mi tvp4511)  

Short Communications

Transformations of the simplest nonsymmetric random walks and some applications of the invariance principle

I. S. Borisov

Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences, Novosibirsk

Abstract: We derive convenient formulas for the tail probabilities of the supnorm of the simplest nonsymmetric random walks defined on a finite time-interval. Using these formulas, we obtain a new representation for the distribution of the number of crossings of a canonical strip by the random walks. As a consequence of the above-mentioned results, we propose a new approach to calculation of the distributions of some boundary functionals of a Wiener process with drift.

Keywords: simplest random walk; Wiener process with drift; distribution of the number of crossings of a strip; invariance principle.

DOI: https://doi.org/10.4213/tvp4511

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English version:
Theory of Probability and its Applications, 2014, 58:2, 323–329

Bibliographic databases:

MSC: 60
Received: 28.02.2012

Citation: I. S. Borisov, “Transformations of the simplest nonsymmetric random walks and some applications of the invariance principle”, Teor. Veroyatnost. i Primenen., 58:2 (2013), 381–387; Theory Probab. Appl., 58:2 (2014), 323–329

Citation in format AMSBIB
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