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arXiv · 0912.2665

A Pluzhnikov's Theorem, Brownian motions and Martingales in Lie Group with skew-symmetric connections

S. N. Stelmastchuk
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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.

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S. N. Stelmastchuk. 2009-12-14. A Pluzhnikov's Theorem, Brownian motions and Martingales in Lie Group with skew-symmetric connections. https://arxiv.org/abs/0912.2665

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