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Local Gaussian modelling of stochastic dynamical systems in the analysis of non-linear random vibrations

Published online by Cambridge University Press:  14 July 2016

Tohru Ozaki
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Abstract

Stochastic dynamical system models for non-linear random vibrations are considered and their discrete-time version, non-linear time series models are introduced using the local Gaussian modelling method. Some computational problems and implications of the present method in non-linear time series analysis are discussed.

Keywords

DIFFUSION PROCESSDYNAMICS OF MOORED VESSELLOCAL LINEARIZATIONNON-LINEAR MARKOVIAN REPRESENTATIONAUTOREGRESSIVE-MOVING AVERAGE MODELSAMPLITUDE-DEPENDENT AUTOREGRESSIVE MODELS
Type
Part 4—Non-linear and Non-stationary Systems in Time Series
Information
Journal of Applied Probability , Volume 23 , Issue A: Essays in Time Series and Allied Processes , 1986 , pp. 241 - 255
Copyright
Copyright © 1986 Applied Probability Trust 

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References

Akaike, H. (1974) Markovian representation of stochastic processes and its application to the analysis of autoregressive moving average processes. Ann. Inst. Statist. Math. 26, 363–387.CrossRefGoogle Scholar
Bartlett, M. S. (1946) On the theoretical specification and sampling properties of autocorrelated time series. J. R. Statist. Soc. B8, 27–41.Google Scholar
Caughey, T. K. (1963) Derivation and application of the Fokker-Planck equation to discrete nonlinear dynamic systems subjected to white random excitation. J. Acoust. Soc. Amer. 35, 1683–1692.CrossRefGoogle Scholar
Durbin, J. (1961) Efficient fitting of linear models for continuous stationary time series from discrete data. Bull. Inst. Internat. Statist. 38, 273–282.Google Scholar
Gikhman, I. I. and Skorohod, A. V. (1965) Introduction to the Theory of Random Processes (translated by Scripta Technica, Inc.) W. B. Saunders Company, Philadelphia.Google Scholar
Haggan, V. and Ozaki, T. (1981) Modelling nonlinear random vibrations using an amplitude-dependent autoregressive time series model. Biometrika 68, 189–196.CrossRefGoogle Scholar
Hannan, E. J. (1969) The identification of vector-mixed autoregressive-moving average systems. Biometrika 57, 223–225.Google Scholar
Hannan, E. J. (1970) Multiple Time Series. Wiley, New York.CrossRefGoogle Scholar
Hannan, E. J. (1981) System identification. In Stochastic Systems: The Mathematics of Filtering and Identification and Applications. Proceeding of NATO Advanced Study Institute. D. Reidel, Dordrecht, 221–246.CrossRefGoogle Scholar
Kendall, M. G. (1944) On autoregressive time series. Biometrika 33, 105–122.CrossRefGoogle Scholar
Maruyama, T. (1983) Stochastic theory of population genetics. Bull. Math. Biol. 45, 521–554.CrossRefGoogle Scholar
Ohtsu, K., Horigome, M. and Kitagawa, G. (1979) A new ship's auto pilot design through a stochastic model. Automatica 15, 255–268.CrossRefGoogle Scholar
Otomo, T., Nakagawa, T. and Akaike, H. (1972) Statistical approach to computer control of cement rotary kilns. Automatica 8, 35–48.CrossRefGoogle Scholar
Ozaki, T. (1982) Non-linear threshold autoregressive models for non-linear random vibrations. J. Appl. Prob. 18, 443–451.CrossRefGoogle Scholar
Ozaki, T. (1983) Non-linear time series models and dynamical systems. In Handbook of Statistics 5, ed. Hannan, E. J. et al., North-Holland, Amsterdam.Google Scholar
Pandit, S. M. and Wu, S. M. (1975) Unique estimates of the parameters of a continuous stationary stochastic process. Biometrika 62, 497–501.CrossRefGoogle Scholar
Tong, H. and Lim, K. S. (1980) Threshold autoregression, limit cycles and cyclical data. J. R. Statist. Soc. B42, 245–292.Google Scholar
Yule, G. U. (1927) On a method of investing periodicities in disturbed series, with special reference to Wolfer's sunspot numbers. Phil. Trans. R. Soc. London A226, 267–298.Google Scholar