## 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.

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December 11, 2009

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