Characterization of multivariate stationary Gaussian reciprocal diffusions (Q1365551)

\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.