Brownian motion on the Wiener sphere and the infinite-dimensional Ornstein-Uhlenbeck process

The infinite-dimensional Ornstein-Uhlenbeck process a is constructed from Brownian motion on the infinite-dimensional sphere SN-1(1) (the Wiener sphere) - or equivalently, by rescaling on SN-1(root N) - which is defined for infinite N by nonstandard analysis. This gives rigorous sense to the informal idea (due to Malliavin, Williams and others) that a can he thought of as Brownian motion on S-infinity(root infinity). An invariance principle follows easily. The paper is a sequel to Cutland and Ng (1993) where the uniform Loeb measure on SN-1(1) was shown to give a rigorous construction of Wiener measure. (C) 1999 Elsevier Science B.V. All rights reserved.