Dilations of -bounded stochastic processes indexed by a locally compact group

Author:
Kari Ylinen

Journal:
Proc. Amer. Math. Soc. **90** (1984), 378-380

MSC:
Primary 43A30; Secondary 60G12

MathSciNet review:
728352

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Abstract: It is proved that a stochastic process (i.e., a Hilbert space valued function) indexed by a locally compact group is -bounded (i.e., weakly harmonizable in an appropriate sense) if, and only if, it can be expressed as an orthogonal projection of a process whose covariance function satisfies for some continuous positive-definite function . The result generalizes a well-known theorem due to H. Niemi, and depends on the noncommutative Grothendieck type inequality of G. Pisier.

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DOI:
https://doi.org/10.1090/S0002-9939-1984-0728352-4

Article copyright:
© Copyright 1984
American Mathematical Society