Müntz linear transforms of Brownian motion

Larbi Alili (University of Warwick)
Ching-Tang Wu (National Taitung University)


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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Pages: 1-15

Publication Date: March 22, 2014

DOI: 10.1214/EJP.v19-2424


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