Electronic Communications in Probability

BV-regularity for the Malliavin derivative of the maximum of the Wiener process

Dario Trevisan

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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.

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Electron. Commun. Probab., Volume 18 (2013), paper no. 29, 9 pp.

Accepted: 16 April 2013
First available in Project Euclid: 7 June 2016

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Zentralblatt MATH identifier

Primary: 60H07: Stochastic calculus of variations and the Malliavin calculus
Secondary: 28C20: Set functions and measures and integrals in infinite-dimensional spaces (Wiener measure, Gaussian measure, etc.) [See also 46G12, 58C35, 58D20, 60B11]

Malliavin Calculus BV functions

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Trevisan, Dario. BV-regularity for the Malliavin derivative of the maximum of the Wiener process. Electron. Commun. Probab. 18 (2013), paper no. 29, 9 pp. doi:10.1214/ECP.v18-2314. https://projecteuclid.org/euclid.ecp/1465315568

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