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

Author: Peggy Tang Strait
Journal: Proc. Amer. Math. Soc. 33 (1972), 207-209
MSC: Primary 60.62
MathSciNet review: 0290465
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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 [Enhancements On Off] (What's this?)

  • [1] Paul Lévy, Le mouvement brownien, Mémor. Sci. Math., no. 126, Gauthier-Villars, Paris, 1954 (French). MR 0066588
  • [2] Peggy Tang Strait, Sample function regularity for Gaussian processes with the parameter in a Hilbert space, Pacific J. Math. 19 (1966), 159–173. MR 0198537

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Keywords: Lévy's Brownian process, Hilbert sphere, sample function continuity, unbounded sample functions
Article copyright: © Copyright 1972 American Mathematical Society

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