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.References
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Additional Information
- © Copyright 1987 American Mathematical Society
- 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