M\"untz linear transforms of Brownian motion
Probability
2014-04-01 v4
Abstract
We consider a class of linear Volterra transforms of Brownian motion associated to a sequence of M\"untz Gaussian spaces and determine explicitly their kernels; some interesting links with M\"untz-Legendre polynomials are provided. This gives new explicit examples of progressive Gaussian enlargement of the Brownian filtration. By exploiting a link to stationarity, we give a necessary and sufficient condition for the existence of kernels of infinite order associated to an infinite dimensional M\"untz Gaussian space; we also examine when the transformed Brownian motion remains a semimartingale in the filtration of the original process.
Cite
@article{arxiv.1112.4071,
title = {M\"untz linear transforms of Brownian motion},
author = {Larbi Alili and Ching-Tang Wu},
journal= {arXiv preprint arXiv:1112.4071},
year = {2014}
}