preprint
Inserted: 10 jun 2017
Year: 2012
Abstract:
We define a capacity C on abstract Wiener spaces and prove that, for any u
with bounded variation, the total variation measure
Du
is absolutely
continuous with respect to C: this enables us to extend the usual rules of
calculus in many cases dealing with BV functions. As an application, we show
that, on the classical Wiener space, the random variable sup{0\leqt\leqT} Wt
admits a measure as second derivative, whose total variation measure is
singular w.r.t. the Wiener measure.