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
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  where . The integral test obtained involves the index of a mean zero Gaussian measure on the Banach space, which is due to Kuelbs . The special case that when is itself a real separable Hilbert space is also illustrated.
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