Abstract
We show that, on the classical Wiener space, the random variable $M = \sup_{0\le t \le T} W_t$ admits a measure as second Malliavin derivative, whose total variation measure is finite and singular w.r.t. the Wiener measure.
Citation
Dario Trevisan. "BV-regularity for the Malliavin derivative of the maximum of the Wiener process." Electron. Commun. Probab. 18 1 - 9, 2013. https://doi.org/10.1214/ECP.v18-2314
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