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Evolution of the nth probability density and entropy function in stochastic systems

✍ Scribed by Riccardo Riganti

Publisher
Elsevier Science
Year
1988
Tongue
English
Weight
722 KB
Volume
30
Category
Article
ISSN
0378-4754

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✦ Synopsis

The time evolution of dynamical systems with random initial conditions is considered, by deriving the n th order probability density of the stochastic process which describes the response of the system, and the entropy function related to the said distibution. A constructive theorem is proved, which enables the explicit calculation of the nth order probability density in terms of the statistics of the initial conditions. Some monotonicity properties of the entropy are derived, and the results are applied in two examples. The same analysis can be applied to the study of the probabilistic response of dynamical systems with constant random parameters and deterministic initial conditions.

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