2016/07/19 by Levi Lopes de Lima, de Lima, Levi Lopes
Mathematics · #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Mathematical Dynamics and Fractals #Primary: 58J65 #Probability (math.PR) #Secondary: 60J65 #Stochastic processes and statistical mechanics
paper · pdf · doi:10.48550/arxiv.1607.05646
openalex publication_date 2016/07/19 · openalex created_date 2022/10/03 · openalex updated_date 2026/07/28
We establish an integral test describing the exact cut-off between recurrence\nand transience for normally reflected Brownian motion in certain unbounded\ndomains in a class of warped product manifolds. Besides extending a previous\nresult by R. Pinsky, who treated the case in which the ambient space is flat,\nour result recovers the classical test for the standard Brownian motion in\nmodel spaces. Moreover, it allows us to discuss the recurrence/transience\ndichotomy for certain generalized tube domains around totally geodesic\nsubmanifolds in hyperbolic space.\n