Electronic Journal of Probability
- Electron. J. Probab.
- Volume 17 (2012), paper no. 22, 14 pp.
Predictable projections of conformal stochastic integrals: an application to Hermite series and to Widder's representation
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.
Electron. J. Probab., Volume 17 (2012), paper no. 22, 14 pp.
Accepted: 14 March 2012
First available in Project Euclid: 4 June 2016
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
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]
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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