On consistent estimators of a usefull signal in the linear one-dimensional stochastic model when an expectation of the transformed signal does not exist

Author: Gogi Pantsulaia
Co-authors: Zurab Zerakidze, Gimzer Saatashvili
Keywords: useful signal, consistent estimator
Annotation:

The separation problem for a family of Borel and Baire -powers of shift-measures on is studied for an arbitrary infinite additive group using the technique developed in [Kuipers L., Niederreiter H., Uniform distribution of sequences, John Wiley& Sons, N.Y.:London. Sidney., Toronto, 1974], [Shiryaev A.N., Probability (in Russian), Izd.``Nauka", Moscow, 1980] and [Pantsulaia G.R., Invariant and quasiinvariant measures in infinite-dimensional topological vector spaces, Nova Science Publishers, Inc., New York, 2007]. It is proved that defined by for , is a consistent estimator of a useful signal in the one-dimensional linear stochastic model where is a counting measure and is a sequence of independent identically distributed random variables on with a strictly increasing continuous distribution function and the expectation of does not exist.

Lecture files:

Gogi-Pantsulaia-GEO.pdf [ka]
Gogi-Pantsulaia-ENG.pdf [en]