Random process representations of chaos

There may be some disagreements to use chaos in application, for its characteristics are not very clear when applying them in real application. Chaos is generally characterized as a nonlinear, deterministic phenomenon. For a common type of chaotic systems, this paper introduces equivalent descriptions in the form of random process with a study research of different random distributions inputs. Such models have many advantages as they much better provide a bridge between chaos and random process. The outputs of this system will be shown to be the random process representation of corresponding chaotic system. Specifically, for a given random distribution inputs, such system will generate exactly the outputs which can obey almost the same distribution as its inputs through the corresponding chaotic map with certain initial condition.