Polynomial approximation for a class of physical random variables

De Santis, A.; Gandolfi, A.; Germani, A.; Tardelli, P.

doi:10.1090/S0002-9939-1994-1164142-5

Polynomial approximation for a class of physical random variables
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by A. De Santis, A. Gandolfi, A. Germani and P. Tardelli

Proc. Amer. Math. Soc. 120 (1994), 261-266

DOI: https://doi.org/10.1090/S0002-9939-1994-1164142-5

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Abstract:

In white noise theory on Hilbert spaces, it is known that maps which are uniformly continuous around the origin in the S-topology constitute an important class of "physical" random variables. We prove that random variables having such a continuity property can be approximated in the gaussian measure by polynomial random variables. The proof relies on representing functions which are uniformly S-continuous around the origin as the composition of a continuous map with a Hilbert-Schmidt operator.

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