The Sequences with Stationary differences
Keywords:
difference equation; stationary increment; the correlation function; the correlation difference; spectral expansion; harmonizable; non-stationarity rank
Abstract
This paper studies nonstationary random sequences with stationary increments. General representations are obtained for their correlation function and correlation differences. The general case is studied for non-stationary sequence, which is the solution of difference equation with stationary right-hand side. Derived spectral representations prove that such sequences are harmonizable. The general representation of solution correlation function is obtained for equation, the right-hand side of which is a non-stationary sequence of finite non-stationarity rank.
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References
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Livshits M.S.; Yantsevich A.A. Operator Colligations in Hilbert Spaces / M. S. Livshits; A. A.Yantsevich. – New York: Wiley and Sons, 1979. – 211 pp.
Yantsevich A .A. Nonstationary Sequence in Hilbert Space I . Correlation theory // Journal of Soviet Mathematics. 1990. – vol. 48, No. 5. – P. 615 – 618.
A. A. Yantsevitch, A. Yu. Petrova. The spectral theory of some classes of random vector functions. // Radioelectronics and informatics, Kh. KNURE – 2007. – P. 37-40.
Ye. A. Kogut, Z. F. Nazyrov, A. A. Yantsevitch. About some class of linear discrete systems. // Bulletin of V. Karazin Kharkiv National University, – 2012. Series «Mathematical Modelling. Information Technology. Automated Control Systems», Issue 20. – P. 92-102.
A. V. Korobskaia, Z. F. Nazyrov, A. A. Yantsevitch. A class of revolutionarily representable random processes. // Bulletin of V. Karazin Kharkiv National University, – 2012. Series «Mathematical Modelling. Information Technology. Automated Control Systems», Issue 19. – P. 184-197.
Peterson A; Schneider J. The Cauchy Function for Order Linear Difference Equations // Journal Of Mathematics. 1995. – Volume 25, Number 1 Winter.
Rooznov Ju. A. Stationary Random Processes / Ju. A. Rooznov. – Moscow: Fizmatgiz, 1963.
Cheremskaya N. V. Linear Transformations of Nonstationary Stochastic Sequences. // Radiotekhneka. – 2004. – vol 136. – P. 43-49 (Russian).
Loève M. Probability Theory / M. Loève. – Prinston, 1955. – 719 pp.
Published
2014-03-11
How to Cite
Assadi, S., Jouja, G., & Farhood, F. (2014). The Sequences with Stationary differences. Bulletin of V.N. Karazin Kharkiv National University, Series «Mathematical Modeling. Information Technology. Automated Control Systems», 25(1131), 201-210. Retrieved from https://periodicals.karazin.ua/mia/article/view/14242
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