Electronic Journal of Probability

Predictable projections of conformal stochastic integrals: an application to Hermite series and to Widder's representation

Matteo Casserini and Freddy Delbaen

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Abstract

In this article, we study predictable projections of stochastic integrals with respect to the conformal Brownian motion, extending the connection between powers of the conformal Brownian motion and the corresponding Hermite polynomials. As a consequence of this result, we then investigate the relation between analytic functions and $L^p$-convergent series of Hermite polynomials. Finally, our results are applied to Widder's representation for a class of Brownian martingales, retrieving a characterization for the moments of Widder's measure.

Article information

Source
Electron. J. Probab., Volume 17 (2012), paper no. 22, 14 pp.

Dates
Accepted: 14 March 2012
First available in Project Euclid: 4 June 2016

Permanent link to this document
https://projecteuclid.org/euclid.ejp/1465062344

Digital Object Identifier
doi:10.1214/EJP.v17-1883

Mathematical Reviews number (MathSciNet)
MR2900463

Zentralblatt MATH identifier
1258.60035

Subjects
Primary: 60H05: Stochastic integrals
Secondary: 60H30: Applications of stochastic analysis (to PDE, etc.) 60G46: Martingales and classical analysis 33C45: Orthogonal polynomials and functions of hypergeometric type (Jacobi, Laguerre, Hermite, Askey scheme, etc.) [See also 42C05 for general orthogonal polynomials and functions]

Keywords
Predictable projections stochastic integrals conformal Brownian motion Hermite polynomials Brownian martingales Widder's representation

Rights
This work is licensed under aCreative Commons Attribution 3.0 License.

Citation

Casserini, Matteo; Delbaen, Freddy. Predictable projections of conformal stochastic integrals: an application to Hermite series and to Widder's representation. Electron. J. Probab. 17 (2012), paper no. 22, 14 pp. doi:10.1214/EJP.v17-1883. https://projecteuclid.org/euclid.ejp/1465062344


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