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2014 Müntz linear transforms of Brownian motion
Larbi Alili, Ching-Tang Wu
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Electron. J. Probab. 19: 1-15 (2014). DOI: 10.1214/EJP.v19-2424


We consider a class of Volterra linear transforms of Brownian motion associated to a sequence of Müntz Gaussian spaces and determine explicitly their kernels; the kernels take a simple form when expressed in terms of Müntz-Legendre polynomials. These are new explicit examples of progressive Gaussian enlargement of a Brownian filtration. We give a necessary and sufficient condition for the existence of kernels of infinite order associated to an infinite dimensional Müntz Gaussian space; we also examine when the transformed Brownian motion remains a semimartingale in the filtration of the original process. This completes some already obtained partial answers to the aforementioned problems in the infinite dimensional case.


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Larbi Alili. Ching-Tang Wu. "Müntz linear transforms of Brownian motion." Electron. J. Probab. 19 1 - 15, 2014.


Accepted: 22 March 2014; Published: 2014
First available in Project Euclid: 4 June 2016

zbMATH: 1292.60079
MathSciNet: MR3183580
Digital Object Identifier: 10.1214/EJP.v19-2424

Primary: 45D05
Secondary: 60G15

Keywords: Enlargement of filtration , Gaussian process , M\"untz polynomials , noncanonical representation , self-reproducing kernel , Volterra representation


Vol.19 • 2014
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