Relatório de pesquisa 32/09


A Pluzhnikov´s Theorem, Brownian Motions and Martingales in Lie Group with Skew-Symmetric Connections, Simão Stelmastchuk, submitted December 11, 2009.

Abstract
Let $G$ be a Lie Group with a left invariant connection such that its connection function is skew-symmetric. Our main goal is to show a version of Pluzhnikov's Theorem for this kind of connection. To this end, we use the stochastic logarithm. More exactly, the stochastic logarithm gives characterizations for Brownian motions and Martingales in $G$, and these characterzations are used to prove Pluzhnikov's Theorem.


Mathematics Subject Classifications (2000):  53C43, 58E20,  58J65, 60H30, 60G48

Keywords: 
harmonic maps; Lie groups; stochastic analisys on manifolds.


Copy of the file:

rp32-09.pdf (PDF)

December 11, 2009

 

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