Positive definite kernels on the set of integers, stability, some properties and applications. (English) Zbl 07858109
Summary: We define and investigate a class of positive definite kernel, a 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 the Kolmogorov decomposition. Finally, some applications to stochastic processes are given.
MSC:
42A82 | Positive definite functions in one variable harmonic analysis |
60G10 | Stationary stochastic processes |