Positive definite kernels on the set of integers, stability, some properties and applications
DOI:
https://doi.org/10.24193/subbmath.2022.4.13Keywords:
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.
Mathematics Subject Classification (2010): 42A82, 60G10.
Received 14 February 2020; Accepted 13 April 2020.
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