On the justification of Gaussian heuristic method in the theory of random vibration

Abstract

Recently in the problems of random vibration, the heuristic method, in which output process is supposed to be Gaussian when Gaussian input process is given, is applied [1, 2]. This method is called the “Gaussian heuristic method”. This paper deals with the justification of “Gaussian heuristic method”, form that two following important conclusions are proved:

- “Gaussian heuristic method” gives density function of probability with the first order approximation with respect to the small parameter ε.

- Applying this method we get mean values and second order correlation functions in second order approximation with respect to the small parameter ε.