Geodesic
Combinatorial methods for investigating the distribution of the trajectory amplitude of a random walk
Sbornik. Mathematics, Tome 18 (1972) no. 3, pp. 529-540 Cet article a éte moissonné depuis la source Math-Net.Ru

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Exact formulas are derived for the number of trajectories of a Bernoulli random walk which have a fixed number of successes and predetermined maximum and minimum values. The asymptotic distribution is found for the indeterminate part of the amplitude for large deviations. The exact distribution of the trajectory amplitude of a Wiener process is also found and investigated. Bibliography: 4 titles. 
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     title = {Combinatorial methods for investigating the distribution of the trajectory amplitude of a~random walk},
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V. K. Zakharov; O. V. Sarmanov. Combinatorial methods for investigating the distribution of the trajectory amplitude of a random walk. Sbornik. Mathematics, Tome 18 (1972) no. 3, pp. 529-540. http://geodesic.mathdoc.fr/item/SM_1972_18_3_a7/

[1] V. K. Zakharov, O. V. Sarmanov, “Mnogomernye zakony raspredeleniya maksimumov otrezkov traektorii sluchainogo bluzhdaniya”, Zh. vych. matem. i matem. fiziki, 11:6 (1971), 1526–1543

[2] W. Feller, “The asymptotic distribution of the range of sums of independent random variables”, Ann. Math. Stat., 22:3 (1951), 427–432 | DOI | MR | Zbl

[3] G. Beitmen, A. Erdeii, Vysshie transtsendentnye funktsii, t. 3, Nauka, Moskva, 1967 | MR

[4] V. K. Zakharov, O. V. Sarmanov, “Asimptoticheskie metody issledovaniya peresechenii gaussovskogo markovskogo protsessa s zadannym urovnem”, Zh. vych. matem. i matem. fiziki, 8:3 (1968), 600–615 | MR | Zbl