Müntz linear transforms of Brownian motion

Details Müntz linear transforms of Brownian motion Müntz linear transforms of Brownian motion

2011-12-17

arxiv.org/abs/1112.4071v1

Mathematics

Probability

Scientific paper

We consider a class of linear Volterra transforms and determine explicitly the kernels from the spaces that they reproduce. The kernels resemble M\"untz-Legendre polynomials to which they are very related. A link between these self-reproducing kernels and reproducing kernel systems, alias. kernel systems, is outlined. As a consequence, some properties of M\"untz kernels are, in fact, inherited from the corresponding kernel systems. This combined with the link to stationary processes is exploited to find a necessary and sufficient condition for existence of M\"untz kernels of infinite order.

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