@article{EJP2424,
author = {Larbi Alili and Ching-Tang Wu},
title = {Müntz linear transforms of Brownian motion},
journal = {Electron. J. Probab.},
fjournal = {Electronic Journal of Probability},
volume = {19},
year = {2014},
keywords = {Enlargement of filtration ; Gaussian process ; M\\"untz polynomials ; noncanonical representation ; self-reproducing kernel ; Volterra representation},
abstract = {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.},
pages = {no. 36, 1-15},
issn = {1083-6489},
doi = {10.1214/EJP.v19-2424},
url = {http://ejp.ejpecp.org/article/view/2424}}