Characterization of multivariate stationary Gaussian reciprocal diffusions
type: Item
instance of: scholarly article
title: Characterization of multivariate stationary Gaussian reciprocal diffusions
zbMATH Open document ID: 0883.60027
author: Bernard C. Levy
published in: Journal of Multivariate Analysis
publication date: 1998-03-16T00:00:00Z
review text: \textit{B. Jamison}'s [Ann. Math. Stat. 41, 1624-1630 (1970; Zbl 0248.60030)] classification (in terms of the covariance function) of stationary scalar Gaussian reciprocal processes over a finite interval -- amended by \textit{S. C. Chay} [J. Multivariate Anal. 2, 14-76 (1972; Zbl 0228.60017)] and by \textit{J.-P. Carmichael}, \textit{J.-C. Massé} and \textit{R. Theodorescu} [C. R. Acad. Sci., Paris, Sér. I 295, 291-293 (1982; Zbl 0506.60031)] -- is extended to a certain class of multivariate Gaussian reciprocal diffusions. Their covariance functions are characterized by using the eigenstructure of a Hamiltonian matrix leading to a parametrization of these functions.
Mathematics Subject Classification ID: 60G10
Mathematics Subject Classification ID: 60G15
Mathematics Subject Classification ID: 60G60
Mathematics Subject Classification ID: 60J60
Mathematics Subject Classification ID: 15A21
zbMATH DE Number: 1057404
zbMATH Keywords: Gaussian reciprocal diffusion
zbMATH Keywords: reciprocal process
zbMATH Keywords: Hamiltonian matrix
zbMATH Keywords: stationary process
reviewed by: Radu Theodorescu
MaRDI profile type: Publication
OpenAlex ID: W2067447669
cites work: Reciprocal Processes: The Stationary Gaussian Case
cites work: Q3234472
cites work: Reciprocal processes
cites work: Q5636107
cites work: Q4743505
cites work: Some comments on conditionally Markov and reciprocal Gaussian processes (Corresp.)
cites work: Multivariate reciprocal stationary Gaussian processes
cites work: Reciprocal covariance solutions of some matrix differential equations
cites work: Gaussian reciprocal processes and self-adjoint stochastic differential equations of second order
cites work: Modeling and estimation of discrete-time Gaussian reciprocal processes
cites work: Gaussian reciprocal processes revisited
cites work: Gaussian reciprocal diffusions and positive definite sturm-liouville operators
cites work: Second-Order Markov and Reciprocal Stationary Gaussian Processes
cites work: On Miroshin’s Second-Order Reciprocal Processes
cites work: Reciprocal diffusions and stochastic differential equations of second order∗
cites work: Dynamics and kinematics of reciprocal diffusions
cites work: Gaussian reciprocal diffusions and their associated conservation laws
cites work: Q3974810
cites work: First Passage Time for a Particular Gaussian Process
cites work: Normal forms of elements of classical real and complex Lie and Jordan algebras
cites work: Q5668037
cites work: Canonical forms for symplectic and Hamiltonian matrices
cites work: Q4148103
cites work: Fast projection methods for minimal design problems in linear system theory
cites work: Matrix Analysis
cites work: Realization Theory for Multivariate Stationary Gaussian Processes
cites work: Reciprocal Realizations on the Circle
DOI: 10.1006/JMVA.1997.1678
description: scientific article; zbMATH DE number 1057404