On a class of quaternionic positive definite functions and their derivatives

Daniel Alpay; Fabrizio Colombo; Irene Sabadini

doi:10.1063/1.4977082

On a class of quaternionic positive definite functions and their derivatives

Daniel Alpay, Fabrizio Colombo, Irene Sabadini

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8 Scopus citations

Abstract

In this paper, we start the study of stochastic processes over the skew field of quaternions. We discuss the relation between positive definite functions and the covariance of centered Gaussian processes and the construction of stochastic processes and their derivatives. The use of perfect spaces and strong algebras and the notion of Fock space are crucial in this framework.

Original language	English
Article number	033501
Journal	Journal of Mathematical Physics
Volume	58
Issue number	3
DOIs	https://doi.org/10.1063/1.4977082
State	Published - 1 Mar 2017
Externally published	Yes

ASJC Scopus subject areas

Statistical and Nonlinear Physics
Mathematical Physics

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AB - In this paper, we start the study of stochastic processes over the skew field of quaternions. We discuss the relation between positive definite functions and the covariance of centered Gaussian processes and the construction of stochastic processes and their derivatives. The use of perfect spaces and strong algebras and the notion of Fock space are crucial in this framework.

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On a class of quaternionic positive definite functions and their derivatives

Abstract

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