Martingales in Reductive Homogeneous spaces

2011/06/30 by S. N. Stelmastchuk, Stelmastchuk, S. N.
Mathematics · #22F30 #58J65 #60G48 #60H30 #FOS: Mathematics #Probability (math.PR) #math.PR #msc:22F30 #msc:58J65 #msc:60G48 #msc:60H30

paper · pdf · doi:10.48550/arxiv.1106.6246

10 pages. In this version we correct some mistakes and we improve the results

arxiv created 2014/04/03 · arxiv updated 2014/04/04

Abstract

The subject of this work is to study martingales in a reductive homogeneous space with respect to a symmetric connection. Our basic idea is to view homogenous spaces as principal fiber bundles and, thus, to study martingales on homogeneous space with aid of horizontal martingales on Lie group. Furthermore, using the stochastic logarithm we give a characterization of martingales on homogenous space. To end, we study the martingales in spheres Sⁿ and SL(n,ℝ)/SO(n,ℝ), n ≥ 2.

Related

• Martingales on Principal Fiber Bundles
• Martingale transform and Lévy Processes on Lie Groups
• Martingale dimensions for a class of metric measure spaces
• Sharp martingale inequalities and applications to Riesz transforms on manifolds, Lie groups and Gauss space
• Stochastic areas, Horizontal Brownian Motions, and Hypoelliptic Heat Kernels