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

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.

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Year of publication:	2007
Authors:	De Gregorio, A. ; Orsingher, E.
Published in:	Statistics & Probability Letters. - Elsevier, ISSN 0167-7152. - Vol. 77.2007, 7, p. 667-680
Publisher:	Elsevier
Keywords:	Bessel functions First-passage times Maximal distributions First returns to the origin Random flights Stirling's formula

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Type of publication:	Article
Source:	RePEc - Research Papers in Economics

Persistent link: https://www.econbiz.de/10005137748