The divergence of Banach space valued random variables on Wiener space

Details The divergence of Banach space valued random variables on Wiener space The divergence of Banach space valued random variables on Wiener space

2003-12-25

arxiv.org/abs/math/0312455v2

Probability Theory and Related Fields, vol. 132, no. 2, pp. 291-320, June 2005

Mathematics

Probability

an arXiv link to a corrigendum has been added, see arXiv:0710.4483

Scientific paper

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.

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