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Acta Mathematica Vietnamica

Banach space valued Brownian motions

icon-email NGUYỄN VĂN THU

Abstract

It is known ([1], [3]) that every real Brownian motion B(t), t[0,1], can be represented as B(t)=nZn0tgn(s)ds where {Zn} is a sequence of i.i.d. symmetric Gaussian random variables, {gn} a CONS in L2[0,1] and the series is convergent with probability one uniformly over [0,1]. The aim of the present paper is to prove some complete analogues if this fact for Banach space valued Brownian motions.