Limiting angle of brownian motion in certain two-dimensional Cartan-Hadamard manifolds
نویسنده
چکیده
Suppose that IH is a two-dimensional Cartan-Hadamard manifold with sectional curvatures satisfying a weak negative upper bound and no lower bound. Then the angular part of Brownian motion on IH tends to a limit as time tends to the explosion time of the Brownian motion. Moreover this limit angle has a distribution whose closed support is dense on the circle at infinity. KEY-WORDS : Brownian motion, Cartan-Hadamard manifold, comparison arguments, geodesic, limiting angle, sectional curvature, stochastic differential equations. Subject Classification 60J65, 58G32
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