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

Arnaldo De La Barrera; Osmin Ferrer; José Sanabria

doi:10.24193/subbmath.2022.4.13

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

Authors

Arnaldo De La Barrera Universidad de Pamplona
Osmin Ferrer Universidad de Sucre http://orcid.org/0000-0003-1015-6271
José Sanabria Universidad de Sucre http://orcid.org/0000-0002-9749-4099

DOI:

https://doi.org/10.24193/subbmath.2022.4.13

Keywords:

Positive definite kernels, multivariate stochastic processes, Toepliz kernel, Kolgomorov decomposition.

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.

Downloads

Additional Files

Kernel value operator 2020-04-13

Published

2022-12-01

Issue

Vol. 67 No. 4 (2022)

Section

Articles

License

This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

Transfer of copyright agreement: When the article is accepted for publication, the authors and the representative of the coauthors, hereby agree to transfer to Studia Universitatis Babeș-Bolyai Mathematica all rights, including those pertaining to electronic forms and transmissions, under existing copyright laws, except for the following, which the authors specifically retain: the authors can use the material however they want as long as it fits the NC ND terms of the license. The authors have all rights for reuse according to the license.