A Darling-Siegert formula relating some Bessel integrals and random walks

A. De Gregorio and E. Orsingher

Statistics & Probability Letters, 2007, vol. 77, issue 7, 667-680

Abstract: The combinatorial identityfor , emerging in the study of random flights in the space is examined. A probabilistic interpretation of this formula based on the first-passage time and the time of first return to zero of symmetric random walks is given. A combinatorial proof of this result is also provided. A detailed analysis of the first-passage time distribution is presented together with its fractional counterpart.

Keywords: Bessel; functions; First-passage; times; Maximal; distributions; First; returns; to; the; origin; Random; flights; Stirling's; formula (search for similar items in EconPapers)
Date: 2007
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Citations: View citations in EconPapers (1)

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