Geodesic
Transformations of the simplest nonsymmetric random walks and some applications of the invariance principle
Teoriâ veroâtnostej i ee primeneniâ, Tome 58 (2013) no. 2, pp. 381-387

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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. 
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     author = {I. S. Borisov},
     title = {Transformations of the simplest nonsymmetric random walks and some applications of the invariance principle},
     journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
     pages = {381--387},
     publisher = {mathdoc},
     volume = {58},
     number = {2},
     year = {2013},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TVP_2013_58_2_a8/}
}
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I. S. Borisov. Transformations of the simplest nonsymmetric random walks and some applications of the invariance principle. Teoriâ veroâtnostej i ee primeneniâ, Tome 58 (2013) no. 2, pp. 381-387. http://geodesic.mathdoc.fr/item/TVP_2013_58_2_a8/