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Study of the range process of a Bernoulli random walk. (Étude de l’amplitude d’une marche aléatoire de Bernoulli.) (French) Zbl 0856.60074

Summary: The range process for a symmetric Bernoulli random walk has been studied by P. Vallois and C. S. Tapiero [ibid. 29, No. 1, 1-17 (1995; Zbl 0827.60058)]. They obtained the first two moments of the inverse process. In this note, we obtain the same result by a more direct way. Moreover, the third and fourth centered moments are obtained by the same way and a recurrent relation is given for the probability generating function.

MSC:

60G50 Sums of independent random variables; random walks

Citations:

Zbl 0827.60058