Positive definite kernels on the set of integers, stability, some properties and applications

Abstract

We define and investigate a class of positive  definite  kernel  so called equivalent-kernel. We formulate and prove an analogous  of Paley-Wiener theorem   in the context of  positive  definite  kernel. The main ingredient in the proof is Kolmogorov decomposition. Finally, some  applications to   stochastic processes are given.