Abstract
The problem of describing a dynamic system with random excitation is discussed. A differential equation of any realistic dynamic system has higher derivatives with small coefficients. Besides, the random excitation is not a ‘ white ’ noise, it is a ‘ coloured ’ noise with a small but finite correlation interval. Therefore the system can be described by a many-dimensional Markov process having increased the dimension of the state variable vector. It is found that the Markov process can be reduced if the characteristic time in the system is very long compared with both small parameters and correlation interval in the random forcing. The reduced Markov process can also be represented as a solution of some stochastic differential equation under white-noise excitation. The accuracy of the reduction is illustrated by a numerical example.
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