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Transformations of the simplest nonsymmetric random walks and some applications of the invariance principle. (English) Zbl 1316.60062

Theory Probab. Appl. 58, No. 2, 323-329 (2014); translation from Teor. Veroyatn. Primen. 58, No. 2, 381-387 (2013).
Summary: 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.

MSC:

60G50 Sums of independent random variables; random walks
60F17 Functional limit theorems; invariance principles
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