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arXiv:math/0312455 [math.PR]AbstractReferencesReviewsResources

The divergence of Banach space valued random variables on Wiener space

E. Mayer-Wolf, M. Zakai

Published 2003-12-25, updated 2007-12-20Version 2

The domain of definition of the divergence operator \delta on an abstract Wiener space (W, H, \mu) is extended to include W-valued and W\otimesW-valued "integrands". The main properties and characterizations of this extension are derived and it is shown that in some sense the added elements in \delta'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.

Comments: an arXiv link to a corrigendum has been added, see arXiv:0710.4483
Journal: Probability Theory and Related Fields, vol. 132, no. 2, pp. 291-320, June 2005
Categories: math.PR
Subjects: 60H07, 60H05
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arXiv:0710.4483 [math.PR] (Published 2007-10-24)
Correction to "The divergence of Banach space valued random variables on Wiener space", Prob. Th. Rel. Fields 132, 291-320 (2005)
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