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Brownian motion on a symmetric space of non-compact type: Asymptotic behaviour in polar coordinates. (English) Zbl 0758.58037
This expository paper is a sequel to the author’s paper in [Contemp. Math. 73, 303-332 (1988; Zbl 0658.58041)]. Results of Orihara and Malliavin from the early 1970’s concerning the asymptotic behaviour of Brownian motion on a symmetric space of noncompact type are obtained by a simpler and more direct method. The Brownian motion lives on the set of regular points of the symmetric space, where a skew product representation analogous to polar coordinates is available; asymptotically the ‘radial’ variable tends to infinity almost surely in a precise direction, and the ‘angle’ also converges a.s..
Reviewer: R.Darling

58J65 Diffusion processes and stochastic analysis on manifolds
60J65 Brownian motion
43A85 Harmonic analysis on homogeneous spaces
22E30 Analysis on real and complex Lie groups
60B15 Probability measures on groups or semigroups, Fourier transforms, factorization
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