Abstract
In this paper a random linear system of the form of y(t; ω = ∫ t ∁ K(t, τ; ω)x(τ; ω)dr is studied, where the kernel is a stochastic process defined on a probability space. The concept of the modified characteristic function for the output process is introduced. These characteristic functions are used to identify the distribution of the output process over certain subsets of the probability space, Ω , in order to study the statistical properties of the process. Several examples are given to illustrate the usefulness of the resulting theory. These results extend the previous theory of random linear systems, in that until now, the kernel was deterministic in nature.
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