Reprodusing Kernel Hilbert spaces and their applications in probability and statistics

Abstract

In a large variety of problems in Statistics and Stochastic processes, the random variables which are used do not present finite dimensionality, in contrary their dimension is infinite. On the other hand, the observations of those random variables are actually finitedimensional approximations of corresponding infinite dimensional subjects. Reproducing Kernel Hilbert Spaces (RKHS) are a useful theoretical and practical tool which provides us a series useful representations even for non-linear data. This work will be an introduction to the theory of RKHS in the context of the smoothness of a data set.