A note on Lévy’s Brownian process on the Hilbert sphere

Strait, Peggy Tang

doi:10.1090/S0002-9939-1972-0290465-3

Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

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A note on Lévy’s Brownian process on the Hilbert sphere
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Proc. Amer. Math. Soc. 33 (1972), 207-209 Request permission

Abstract:

Let $X(t)$, t in ${l_2}$, be Lévy’s separable Brownian process. Let S be the unit Hilbert sphere. It is shown that with probability 1, the image of $X(t),t \in S$, is the entire real line.

References

Paul Lévy, Le mouvement brownien, Mémor. Sci. Math., no. 126, Gauthier-Villars, Paris, 1954 (French). MR 0066588
Peggy Tang Strait, Sample function regularity for Gaussian processes with the parameter in a Hilbert space, Pacific J. Math. 19 (1966), 159–173. MR 198537, DOI 10.2140/pjm.1966.19.159