International Journal of Mathematics and Mathematical Sciences

International Journal of Mathematics and Mathematical Sciences / 1979 / Article

Open Access

Volume 2 |Article ID 737165 | https://doi.org/10.1155/S0161171279000491

Mou-Hsiung Chang, "A note on local asymptotic behaviour for Brownian motion in Banach spaces", International Journal of Mathematics and Mathematical Sciences, vol. 2, Article ID 737165, 8 pages, 1979. https://doi.org/10.1155/S0161171279000491

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

Received26 Jul 1978

Abstract

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.

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.


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