Multidimensional random processes with normal covariances. (English) Zbl 0745.60031

The article introduces the concepts of multidimensional locally stationary and normal covariance functions. Necessary and sufficient conditions characterizing these covariances are presented and a close connection with normal operators is established.


60G10 Stationary stochastic processes
Full Text: EuDML Link


[1] R. K. Getor: The shift operator for non-stationary stochastic processes. Duke Math. J. 23 (1965), 175-187.
[2] K. Karhunen: Uber lineare Methoden in der Wahrscheinlichkeitsrechnung. Ann. Acad. Sci. Fenn. Ser. A I Math. 37 (1947), 3-79. · Zbl 0030.16502
[3] M. Loève: Fonctions aléatoires du second ordre. P. Lévy, Processus Stochastiques et Mouvement Brownien. Paris 1948.
[4] J. Michálek: Random sequences with normal covariances. Kybernetika 23 (1987), 6, 443-457. · Zbl 0632.60031
[5] J. Michálek: Locally stationary covariances. Trans. Tenth Prague Conf. on Inform. Theory, Statist. Dec. Functions, Random Processes, Academia, Prague 1988, pp. 83-103. · Zbl 0715.60049
[6] J. Michálek: Normal covariances. Kybernetika 24 (1988), 1, 17-27. · Zbl 0641.60043
[7] Y. A. Rozanov: Stationary random processes. Fizmatgiz, Moscow 1963. In Russian. · Zbl 0152.16302
[8] R. A. Silverman: Locally stationary random processes. IRE Trans. Inform. Theory IT-3 (1957), 3, 182-187.
[9] D. V. Widder: The Laplace Transform. Princeton University Press, Princeton 1946. · Zbl 0060.24801 · doi:10.2307/2305640
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.