Minimal functions, martingales, and Brownian motion on a noncompact symmetric space

Taylor, J. C.

doi:10.1090/S0002-9939-1987-0894445-7

Minimal functions, martingales, and Brownian motion on a noncompact symmetric space
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by J. C. Taylor PDF

Proc. Amer. Math. Soc. 100 (1987), 725-730 Request permission

Abstract:

A Brownian motion on ${{\mathbf {R}}^n}$ may be characterized as a process ${({X_t})_{t \geqslant 0}}$ on a probability space $(\Omega ,\mathfrak {F},P)$ such that, for all $y \in {{\mathbf {R}}^d},\exp \left \{ { - (t/2)||y|{|^2} + \left \langle {y,{X_t}} \right \rangle } \right \}$ is a martingale of expectation one. The analogue of this fact is proved for the Brownian motion on a noncompact symmetric space.

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