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Alili, Larbi; Wu, Ching-Tang (2014)
Publisher: University of Washington. Dept. of Mathematics
Languages: English
Types: Article
Subjects: QA, 60G15, Enlargement of filtration, 45D05, 60G15 (Primary) 26C05, 46E22 (Secondary), Mathematics - Probability, M\"untz polynomials, self-reproducing kernel, noncanonical representation, Volterra representation, 45D05, Gaussian process
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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