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Dilations of $ V$-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
DOI: https://doi.org/10.1090/S0002-9939-1984-0728352-4
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 $ V$-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 $ R$ satisfies $ R(s,t) = \rho ({t^{ - 1}}s) + \rho (s{t^{ - 1}})$ for some continuous positive-definite function $ \rho $. 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

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