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International Journal of Mathematics and Mathematical Sciences
Volume 2 (1979), Issue 4, Pages 669-676

A note on local asymptotic behaviour for Brownian motion in Banach spaces

Department of Mathematics, The University of Alabama in Huntsville, Huntsville 35807, Alabama, USA

Received 26 July 1978

Copyright © 1979 Hindawi Publishing Corporation. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


In this paper we obtain an integral characterization of a two-sided upper function for Brownian motion in a real separable Banach space. This characterization generalizes that of Jain and Taylor [2] where B=n. The integral test obtained involves the index of a mean zero Gaussian measure on the Banach space, which is due to Kuelbs [3]. The special case that when B is itself a real separable Hilbert space is also illustrated.