Characterization of Multivariate Stationary Gaussian Reciprocal Diffusions

Jamisonʹs classification of scalar stationary Gaussian reciprocal processes is extended to multivariate Gaussian reciprocal diffusions (GRDs). The second-order self-adjoint differential equation satisfied by the covariance of a GRD specifies a Hamiltonian matrix whose eigenstructure is employed to parametrize the covariance of stationary GRDs. Characterizations of the conservation matrix and of the covariance matrix of the end point values of a stationary GRD are also provided.