Dilations of $V$-bounded stochastic processes indexed by a locally compact group
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- by Kari Ylinen PDF
- Proc. Amer. Math. Soc. 90 (1984), 378-380 Request permission
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.References
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Additional Information
- © Copyright 1984 American Mathematical Society
- 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