Electronic Communications in Probability

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

Dario Trevisan

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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.

Article information

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

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

Permanent link to this document
https://projecteuclid.org/euclid.ecp/1465315568

Digital Object Identifier
doi:10.1214/ECP.v18-2314

Mathematical Reviews number (MathSciNet)
MR3056066

Zentralblatt MATH identifier
1309.60054

Subjects
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]

Keywords
Malliavin Calculus BV functions

Rights
This work is licensed under a Creative Commons Attribution 3.0 License.

Citation

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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