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Windings of hyperbolic Brownian motion. (English) Zbl 0902.60065

Yor, Marc (ed.), Exponential functionals and principal values related to Brownian motion. A collection of research papers. Madrid: Univ. Autónoma de Madrid, Departamento de Matemáticas, Biblioteca de la Revista Matemática Iberoamericana. 35-72 (1997).
The hyperbolic Brownian motion is defined as the solution of the stochastic differential equation \(dH_t= {1\over 2} (1- | H_t |^2) dx_t\) with \(z_t\) the standard planar Brownian motion. For this motion the author proves an analogue of M. Yor’s on the index relative to zero of a Brownian loop formed by conditioning the planar Brownian motion to hit its starting point at time 1.
For the entire collection see [Zbl 0889.00015].

MSC:

60J65 Brownian motion
60H10 Stochastic ordinary differential equations (aspects of stochastic analysis)
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