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

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  • Cutland, Nigel J.

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.

Suggested Citation

  • Cutland, Nigel J., 1999. "Brownian motion on the Wiener sphere and the infinite-dimensional Ornstein-Uhlenbeck process," Stochastic Processes and their Applications, Elsevier, vol. 79(1), pages 95-107, January.
    • Handle: RePEc:eee:spapps:v:79:y:1999:i:1:p:95-107
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