On the response of a certain class of systems to random inputs

This paper deals with the connection between vector Markoff processes and the response of a lumped constant parameter linear system composed of a finite number of elements. It was known that if a Gaussian process which is one component of a vector Markoff process passes through such a system, the result is also Gaussian and may be considered as one component of a higher dimensional vector Markoff process. We show that the term Gaussian may be excluded in the above statement. The practical importance of this result is that if one can determine the initial and transition probabilities of this vector Markoff process, one can also determine the complete statistical properties of the output of the system. This further implies that the determination of the properties of the output for the class of not necessarily Gaussian inputs mentioned above is not as difficult as might be expected from the results available for just the first probability distribution for non-Gaussian inputs.