Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

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

 

 

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
DOI: https://doi.org/10.1090/S0002-9939-1972-0290465-3
MathSciNet review: 0290465
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

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

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 60.62

Retrieve articles in all journals with MSC: 60.62


Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1972-0290465-3
Keywords: Lévy's Brownian process, Hilbert sphere, sample function continuity, unbounded sample functions
Article copyright: © Copyright 1972 American Mathematical Society