Schilhabel, T.E. and Harris, C.J.
A probabilistic framework for understanding nonlinear dynamical systems in the Hilbert space.
Proceedings of the 12th International Conference on Systems Engineering ICSE'97
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This paper deals with the probabilistic description of a general a priori unknown linear/nonlinear dynamical physical system in an observer related coordinate system. The example of a point mass interacting with its environment and the corresponding relationship to the description of an observer are used as motivation. A probabilistic formulation follows, leading to a continuity equation for probability distributions over time. The last section then demonstrates how probability densities of the spatial coordinates of the point mass may be decomposed into functions which lead to probability distributions of the velocity of the point mass.
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