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

Nigel J. Cutland

Stochastic Processes and their Applications, 1999, vol. 79, issue 1, 95-107

Abstract: The infinite-dimensional Ornstein-Uhlenbeck process v is constructed from Brownian motion on the infinite-dimensional sphere SN-1(1) (the Wiener sphere) - or equivalently, by rescaling, on - which is defined for infinite N by nonstandard analysis. This gives rigorous sense to the informal idea (due to Malliavin, Williams and others) that v can be thought of as Brownian motion on . 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.

Keywords: Infinite-dimensional; Ornstein-Uhlenbeck; process; Wiener; sphere; Loeb; measure (search for similar items in EconPapers)
Date: 1999
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