Exact solution of some discrete stochastic models with chaos

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Abstract
A class of two-dimensional maps with sensitive dependence on initial conditions introduced by Kaplan and Yorke is studied, including the influence of external noise. Exact solutions of the stochastic equations of motion are obtained and used to calculate moments, correlation functions, and probability densities. The relation of the steady-state probability density and the attractor of the maps is considered. The models are also used to test the applicability of other methods of solution from the theory of stochastic processes.