Calculus of Variations and Geometric Measure Theory

D. Trevisan

BV-capacities on Wiener Spaces and Regularity of the Maximum of the Wiener Process

created by trevisan on 10 Jun 2017



Inserted: 10 jun 2017

Year: 2012

ArXiv: 1204.6652 PDF


We define a capacity C on abstract Wiener spaces and prove that, for any u with bounded variation, the total variation measure
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.