Support properties of Gaussian processes over Schwartz space

Piech, M. Ann

doi:10.1090/S0002-9939-1975-0391242-8

Support properties of Gaussian processes over Schwartz space
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by M. Ann Piech PDF

Proc. Amer. Math. Soc. 53 (1975), 460-462 Request permission

Abstract:

We utilize the concept of an abstract Wiener space to prove a converse to a theorem of Minlos, thereby obtaining necessary and sufficient conditions for a Hilbert subspace of $\mathcal {S}’({{\text {R}}^d})$ to support a given Gaussian process over $\mathcal {S}({{\text {R}}^d})$.

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