Innovation and factorization of the density of a regular PC sequence

• Autorzy: Makagon A.
• Języki publikacji: EN

Abstrakty

EN

In this paper we study an innovation representation of a periodically correlated (PC) sequence and describe the factorization of the densities of a regular PC sequence generated by its innovation. As a byproduct we obtain a certain factorization of vector analytic functions which may be of interest in the theory of Hardy spaces.

Słowa kluczowe

EN

periodically correlated sequence; prediction; innovation process; factorization of analytic vector functions

• Wydawca: Wrocław University of Science and Technology
• Czasopismo: Probability and Mathematical Statistics
• Rocznik: 2015
• Tom: Vol. 35, Fasc. 1
• Strony: 15--30
• Opis fizyczny: Bibliogr. 10 poz.

Twórcy

autor

Makagon A.

• Department of Mathematics, Hampton University, 100 E. Queen St., Hampton, VA 23668, USA

Bibliografia

• [1] J. L. Doob,Stochastic Processes, Wiley, New York 1953.
• [2] E. G. Gladyshev, Periodically correlated random sequences, Soviet Math. 2 (1961), pp.385-388.
• [3] H. L. Hurd, Periodically correlated sequences of less than full rank, J. Statist. Plann. Inference 129 (2005), pp. 279-303.
• [4] H. L. Hurd and A. Miamee, Periodically Correlated Random Sequences: Spectral Theory and Practice, Wiley, 2007.
• [5] A. N. Kolmogorov, Stationary Sequences in Hilbert Space, Moscow Univ. Math. Bull. 2 (1941), pp. 1-40.
• [6] A. Makagon, Stationary sequences associated with a periodically correlated sequence, Probab. Math. Statist. 31 (2) (2011), pp. 263-283.
• [7] A. Makagon and A. Miamee, Spectral representation of periodically correlated sequences, Probab. Math. Statist. 33 (1) (2013), pp. 175-188.
• [8] P. Masani, Recent trends in multivariate prediction theory, in: Multivariate Analysis: Proceedings. International Symposium on Multivariate Analysis. Dayton, Ohio, 1965, P. R. Krishnaiah (Ed.), Academic Press, 1966, pp. 351-382.
• [9] B. Sz.-Nagy and C. Foiaş, Harmonic Analysis of Operators on Hilbert Space, North-Holland, 1970.
• [10] K. Urbanik, Lectures on Prediction Theory, Lecture Notes in Math., Vol. 44, Springer, 1967.

Uwagi

Opracowanie rekordu w ramach umowy 509/P-DUN/2018 ze środków MNiSW przeznaczonych na działalność upowszechniającą naukę (2019).