On Lévy's Brownian motion indexed by elements of compact groups (Q2868724)
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scientific article; zbMATH DE number 6239343
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On Lévy's Brownian motion indexed by elements of compact groups |
scientific article; zbMATH DE number 6239343 |
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On Lévy's Brownian motion indexed by elements of compact groups (English)
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18 December 2013
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positive definite functions
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compact groups
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Lévy's Brownian motion
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Lie groups
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The authors investigate the positive definiteness of the Brownian kernel NEWLINE\[NEWLINEK(x,y)={1\over 2}(d(x,x_0)+ d(y,x 0)- d(x,y))NEWLINE\]NEWLINE on a compact group \(G\) and, in particular, for \(G= \text{SO}(n)\), where \(d(x,y)= E|X_x- X_y|^2\), and the stochastic process \(X\) indexed by the points of a metric space \((X,d)\).
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