Applications of the degree theorem to absolute continuity on Wiener space |
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Authors: | A S Üstünel M Zakai |
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Institution: | (1) E.N.S.T., Départment Réseaux, 46, rue Barrault, F-75634 Paris Cedex 13, France;(2) Department of Electrical Engineering, Technion, 32000 Haifa, Israel |
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Abstract: | Summary Let (,H, P) be an abstract Wiener space and define a shift on byT()=+F() whereF is anH-valued random variable. We study the absolute continuity of the measuresPºT
–1and (
F
P)ºT
1 with respect toP using the techniques of the degree theory of Wiener maps, where
F
=det2(1+F) × Exp{–F–1/2|F|2}.The work of the second author was supported by the fund for promotion of research at the Technion |
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Keywords: | 60G30 60H07 |
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