A Nonlinear Deformation of Wiener Space

Shunlong Luo

Journal of Theoretical Probability, 1998, vol. 11, issue 2, 331-350

Abstract: Abstract Based on the complex hyperbolic geometry associated with discrete series of SU(1, 1), we construct a quasi-invariant and ergodic measure on infinite product of Poincaré disc and a hyperbolic analogue of numerical Wiener space which turns out to be a nonlinear deformation of the Wiener space. An integration by parts formula is established. We also investigate the orthogonal decomposition of the L 2-holomorphic functions which is an analogue of the Wiener–Itô–Segal decomposition. In the zero-curvature and large spin limit, we recover the linear Wiener space.

Keywords: Wiener space; Poincaré disc; Bergman measure; quasi-invariance; ergodicity; integration by parts; orthogonal decomposition (search for similar items in EconPapers)
Date: 1998
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DOI: 10.1023/A:1022623603891

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