Geodesic
Distributions and characterizations associated with a random walk
Zapiski Nauchnykh Seminarov POMI, Probability and statistics. Part 30, Tome 501 (2021), pp. 24-35 
M. Ahsanullah; V. B. Nevzorov; A. V. Stepanov. Distributions and characterizations associated with a random walk. Zapiski Nauchnykh Seminarov POMI, Probability and statistics. Part 30, Tome 501 (2021), pp. 24-35. http://geodesic.mathdoc.fr/item/ZNSL_2021_501_a2/
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     author = {M. Ahsanullah and V. B. Nevzorov and A. V. Stepanov},
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     url = {http://geodesic.mathdoc.fr/item/ZNSL_2021_501_a2/}
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Voir la notice du chapitre de livre provenant de la source Math-Net.Ru

In the present paper, we discuss some properties of the distribution and density of the random direction walk after n steps. We further calculate moments of the random walk and propose some characterizations of its distribution. We illustrate our results by tables and graphs.

[1] M. Ahsanullah, V. M. Nevzorov, Ordered random variables, Nova Science Publishers Inc, New York, USA, 2001 | Zbl

[2] M. Ahsanullah, “Some characterizations of Pearson's two unequal step random walk”, Afrika Statistika, 15:1 (2020), 2263–2273 | DOI | MR | Zbl

[3] J. M. Borwein, A. Straub, J. Wan, W. C. Zudilin, “Densities of short uniform random walks”, Canadian J. Math., 64:5 (2012), 961–990 | DOI | MR | Zbl

[4] J. C. Kluyver, “A local probability problem”, Royal Netherlands Academy of Arts and sciences, 81 (1905), 341–350

[5] Lord Rayleigh, “The problem of random walk”, Nature, 72 (1905), 318

[6] K. Pearson, “The problem of the random walk”, Nature, 72 (1905), 294 | DOI

[7] K. Y. Volkova, M. S. Karakulov, Y. Y. Nikitin, “Goodness of fit tests based on the characterization of uniformity by the ratio of order statistics and their efficiencies”, POMI, 466 (2017), 67–80