Revista Matemática Iberoamericana


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Volume 17, Issue 3, 2001, pp. 587–605
DOI: 10.4171/RMI/305

Published online: 2001-12-31

Non-symmetric hitting distributions on the hyperbolic half-plane and subordinated perpetuities

Paolo Baldi[1], Enrico Cassadio Tarabusi[2], Alessandro Figà-Talamanca[3] and Marc Yor

(1) Università di Roma 'Tor Vergata', Italy
(2) Università di Roma La Sapienza, Italy
(3) Università di Roma La Sapienza, Italy

We study the law of functionals whose prototype is $\int_0^{+\infty}$ $e^{B{_s}^{(\nu)}} dW{_s}{^{(\mu)}}$, where $B^{(\nu)}$, $W^{(\mu)}$ are independent Brownian motions with drift. These functionals appear naturally in risk theory as well as in the study of invariant diffusions on the hyperbolic halfplane. Emphasis is put on the fact that the results are obtained in two independent, very different fashions (invariant diffusions on the hyperbolic halfplane and Bessel processes).

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Baldi Paolo, Cassadio Tarabusi Enrico, Figà-Talamanca Alessandro, Yor Marc: Non-symmetric hitting distributions on the hyperbolic half-plane and subordinated perpetuities. Rev. Mat. Iberoamericana 17 (2001), 587-605. doi: 10.4171/RMI/305