arXiv subjects

E. Mayer-Wolf

Publications and source records attributed to E. Mayer-Wolf.

3 recordsLinked to original sources

arXiv2008

The Clark-Ocone formula for vector valued random variables in abstract Wiener space

The classical representation of random variables as the Ito integral of nonanticipative integrands is extended to include Banach space valued random variables on an abstract Wiener space equipped with a filtration induced by a resolution of the identity on the Cameron-Martin space. The Ito integral is replaced in this case by an extension of the divergence to random operators, and the operators involved in the representation are adapted with respect to this filtration in a suitably defined sense. However, the published paper contains a mistake which restricts the validity of the main result, as described in the added Erratum.

math.PR↗

arXiv2007

The divergence of Banach space valued random variables on Wiener space

The domain of definition of the divergence operator δon an abstract Wiener space (W, H, μ) 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 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.

math.PR↗

arXiv2007

Correction to "The divergence of Banach space valued random variables on Wiener space", Prob. Th. Rel. Fields 132, 291-320 (2005)

As a result of some mistakes discovered in the paper mentioned in the title, Corollaries 3.5 and 3.17a) are withdrawn and a new proof is provided for Proposition 3.14, under the added assumption that the second dual of the underlying Banach space Y possesses the Radon-Nykodim property.

math.PR↗