On a set of transformations of Gaussian random functions

2008/05/14 by Alexander I. Nazarov, Nazarov, A. I.
Mathematics · Economics, Econometrics and Finance · #Probability and Statistical Research #Stochastic processes and financial applications #Mathematical Dynamics and Fractals

paper · pdf · doi:10.48550/arxiv.0805.1967

Abstract

We consider a set of one-dimensional transformations of Gaussian random functions. Under natural assumptions we obtain a connection between L₂-small ball asymptotics of the transformed function and of the original one. Also the explicit Karhunen -- Loéve expansion is obtained for a proper class of Gaussian processes.

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