%0 Journal Article
%T On a set of transformations of Gaussian random functions
%A A. I. Nazarov
%J Mathematics
%D 2008
%I arXiv
%X We consider a set of one-dimensional transformations of Gaussian random functions. Under natural assumptions we obtain a connection between $L_2$-small ball asymptotics of the transformed function and of the original one. Also the explicit Karhunen -- Lo\'eve expansion is obtained for a proper class of Gaussian processes.
%U http://arxiv.org/abs/0805.1967v1