On the asymptotic behavior of a sirnple stochastic-dynamic system

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Abstract
The investigation is concerned with the impact of initial uncertainties on predictions. The problem can be solved exactly for sufficiently simple non-linear systems where an exact solution to the deterministic problem is known. In this paper we shall use the advective equation as an example. It is found that the behavior at large times of the system depends on the initial uncertainty and the nature of the probability density function. In applications it is normally necessary to introduce a closure approximation because exact analytical solutions are unknown. Such a closure scheme based on the neglect of third and higher moments will be used in the example and solutions from the closure scheme will be compared with the exact solutions. It is found that the asymptotic values of the uncertainty may be less than the initial uncertainty.

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