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Characterization of Multivariate Stationary Gaussian Reciprocal Diffusions,

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  • Lévy, Bernard C.
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    Abstract

    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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    Bibliographic Info

    Article provided by Elsevier in its journal Journal of Multivariate Analysis.

    Volume (Year): 62 (1997)
    Issue (Month): 1 (July)
    Pages: 74-99

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    Handle: RePEc:eee:jmvana:v:62:y:1997:i:1:p:74-99

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    Keywords: Gaussian reciprocal diffusions Hamiltonian matrix stationary processes;

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