Hitting times of Brownian motion and the Matsumoto-Yor property on trees

Jacek Wesolowski and Piotr Witkowski

Stochastic Processes and their Applications, 2007, vol. 117, issue 9, 1303-1315

Abstract: The Matsumoto-Yor property in the bivariate case was originally defined through properties of functionals of the geometric Brownian motion. A multivariate version of this property was described in the language of directed trees and outside of the framework of stochastic processes in Massam and Wesolowski [H. Massam, J. Wesolowski, The Matsumoto-Yor property on trees, Bernoulli 10 (2004) 685-700]. Here we propose its interpretation through properties of hitting times of Brownian motion, extending the interpretation given in the bivariate case in Matsumoto and Yor [H. Matsumoto, M. Yor, Interpretation via Brownian motion of some independence properties between GIG and gamma variables, Statist. Probab. Lett. 61 (2003) 253-259].

Keywords: Brownian; motion; Hitting; time; Generalized; inverse; Gaussian; distribution; Gamma; distribution; Independence; properties; Directed; and; undirected; trees (search for similar items in EconPapers)
Date: 2007
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Citations: View citations in EconPapers (4)

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