The divergence of Banach space valued random variables on Wiener space |
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Authors: | E Mayer-Wolf M Zakai |
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Institution: | (1) Department of Mathematics, Technion I.I.T., Haifa, Israel;(2) Department of Electrical Engineering, Technion I.I.T., Haifa, Israel |
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Abstract: | The domain of definition of the divergence operator δ on an abstract Wiener space (W,H,μ) is extended to include W–valued and – valued “integrands”. The main properties and characterizations of this extension are derived and it is shown that in some
sense the added elements in δ’s extended domain have divergence zero. These results are then applied to the analysis of quasiinvariant flows induced by
W-valued vector fields and, among other results, it turns out that these divergence-free vector fields “are responsible” for
generating measure preserving flows.
Mathematics Subject Classification (2000): Primary 60H07, Secondary 60H05
An erratum to this article is available at . |
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Keywords: | Abstract Wiener Space Divergence Flows |
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