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

Author

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  • De Gregorio, A.
  • Orsingher, E.

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.

Suggested Citation

  • De Gregorio, A. & Orsingher, E., 2007. "A Darling-Siegert formula relating some Bessel integrals and random walks," Statistics & Probability Letters, Elsevier, vol. 77(7), pages 667-680, April.
    • Handle: RePEc:eee:stapro:v:77:y:2007:i:7:p:667-680
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    Cited by:

    1. Cammarota, V. & Lachal, A. & Orsingher, E., 2009. "Some Darling-Siegert relationships connected with random flights," Statistics & Probability Letters, Elsevier, vol. 79(2), pages 243-254, January.

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