Characterization of Multivariate Stationary Gaussian Reciprocal Diffusions,
Jamison's 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.
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Volume (Year): 62 (1997)
Issue (Month): 1 (July)
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- Carmichael, J. -P. & Massé, J. -C. & Theodorescu, R., 1991. "Reciprocal covariance solutions of some matrix differential equations," Stochastic Processes and their Applications, Elsevier, vol. 37(1), pages 45-60, February.
- Carmichael, J.P. & MasseÂ´, J.C. & Theodorescu, R., 1987. "Multivariate reciprocal stationary Gaussian processes," Journal of Multivariate Analysis, Elsevier, vol. 23(1), pages 47-66, October.
- Chay, S. C., 1972. "On quasi-Markov random fields," Journal of Multivariate Analysis, Elsevier, vol. 2(1), pages 14-76, March.
- Recoules, Raymond, 1991. "Gaussian reciprocal processes revisited," Statistics & Probability Letters, Elsevier, vol. 12(4), pages 297-303, October.
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