In this paper a topology on Hilbert spaces is defined. The continuity of a map with respect to such a topology is equivalent to the uniform S-continuity around the origin, according to the Gross definition. An example of an application, in which the achieved gives a simple tool for providing the existence of stochastic solutions, is reported for a quite general class of non- linear differential equations driven by white noise.
On the definition of a topology in Hilbert spaces with application to the white noise theory
GERMANI, Alfredo
1983-01-01
Abstract
In this paper a topology on Hilbert spaces is defined. The continuity of a map with respect to such a topology is equivalent to the uniform S-continuity around the origin, according to the Gross definition. An example of an application, in which the achieved gives a simple tool for providing the existence of stochastic solutions, is reported for a quite general class of non- linear differential equations driven by white noise.File in questo prodotto:
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