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A one-dimensional discrete-time dynamics near the onset of deterministic diffusion additively coupled to weak Gaussian white noise is studied. The diffusion coefficient is related to the escape rate out of an interval and a method for the calculation of this rate is introduced which, unlike previous investigations, fully takes into account all relevant escape paths. It is found that the diffusion coefficient of the deterministic dynamics may be considerably reduced by the noise in agreement with numerical simulations. It is shown that certain fundamental problems in the concept of deterministic diffusion without noise do not affect the validity of our result.
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Peter Reimann (1994) studied this question.
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