The von Mises–Fisher distribution of the first exit point from the hypersphere of the drifted Brownian motion and the density of the first exit time

Riccardo Gatto

Statistics & Probability Letters, 2013, vol. 83, issue 7, 1669-1676

Abstract: A characterization is provided for the von Mises–Fisher random variable, in terms of first exit point from the unit hypersphere of the drifted Wiener process. Laplace transform formulae for the first exit time from the unit hypersphere of the drifted Wiener process are provided. Post representations in terms of Bell polynomials are provided for the densities of the first exit times from the circle and from the sphere.

Keywords: Bell polynomial; Bessel function; Directional distribution; Laplace transform; Post inversion formula (search for similar items in EconPapers)
Date: 2013
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DOI: 10.1016/j.spl.2013.03.010

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