This article is cited in 2 papers

Combinatorial methods for investigating the distribution of the trajectory amplitude of a random walk

V. K. Zakharov, O. V. Sarmanov


Abstract: 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.

UDC: 518+519.2

MSC: Primary 60C05, 60J15; Secondary 60F10, 60J65

Received: 06.04.1972

 English version: Mathematics of the USSR-Sbornik, 1972, 18:3, 529–540

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