This paper is concerned with responses of linear systems to non-Gaussian random excitation and with the measurement of the departure of the responses from Gaussian behavior. First, we show the classical Rosenblatt result and its nonapplicability to the most popular practical systems described by differential equations of first and second order. Then, using a simple measure of departure from normality (the asymmetry and excess coefficients) and performing numerical calculations, we give quantitative information about the effect of system parameters and the radius of correlation of the excitation process on the distance from normality.
Key wordsLinear systems random excitation Gaussian processes limit theorems departure from normality
Unable to display preview. Download preview PDF.
- 1.W. Hoeffing and H. Robbins,Duke Math. J. 15:773–780 (1948).Google Scholar
- 2.M. Rosenblatt,Proc. Nat. Acad. Sci. USA 42:43–47 (1956).Google Scholar
- 3.J. A. Rozanov,Probability Theory Appl. 5:243–246 (1960).Google Scholar
- 4.M. RosenblattQuart. Appl. Math. 18:387–393 (1961).Google Scholar
- 5.W. M. Wolkov,Electron. 15(12) (1970).Google Scholar
- 6.A. Papoulis,J. Appl. Probab. 8:118–127 (1971).Google Scholar
- 7.A. Papoulis,IEEE Trans. Inform. Theory IT-18(1):20–23 (1972).Google Scholar
- 8.C. L. Mallows,J. Appl Prob.,4:313–329 (1967).Google Scholar
- 9.K. Sobczyk, The Use of Gaussian Analysis in Non-Gaussian Problems, Department of Mechanical Engineering, Glasgow University (1976).Google Scholar
- 10.Z. Kotulski, Gaussianity in Stochastic Differential Equations (in Polish), M. Sci. thesis, Warsaw Technical University (1979).Google Scholar
- 11.J. L. Lumley, inStatistical Models and Turbulence, Lecture Notes in Physics (Springer, New York, 1972).Google Scholar
- 12.N. N. Kolmogorov and J. A. Rozanov,Probability Theory Appl. 5:222–227 (1960).Google Scholar
- 13.K. Sobczyk and D. B. Macvean inStochastic Problems in Dynamics (Pitman, New York, 1977).Google Scholar