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2012 Predictable projections of conformal stochastic integrals: an application to Hermite series and to Widder's representation
Matteo Casserini, Freddy Delbaen
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Electron. J. Probab. 17: 1-14 (2012). DOI: 10.1214/EJP.v17-1883

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.

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Matteo Casserini. Freddy Delbaen. "Predictable projections of conformal stochastic integrals: an application to Hermite series and to Widder's representation." Electron. J. Probab. 17 1 - 14, 2012. https://doi.org/10.1214/EJP.v17-1883

Information

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

zbMATH: 1258.60035
MathSciNet: MR2900463
Digital Object Identifier: 10.1214/EJP.v17-1883

Subjects:
Primary: 60H05
Secondary: 33C45 , 60G46 , 60H30

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

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