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


Author: J. C. Taylor
Journal: Proc. Amer. Math. Soc. 100 (1987), 725-730
MSC: Primary 60B15; Secondary 58G32, 60G44, 60J65
DOI: https://doi.org/10.1090/S0002-9939-1987-0894445-7
MathSciNet review: 894445
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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)\vert\vert y\vert{\vert^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.


References [Enhancements On Off] (What's this?)

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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1987-0894445-7
Article copyright: © Copyright 1987 American Mathematical Society

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