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

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  • Riganti, Riccardo

Abstract

The time evolution of dynamical systems with random initial conditions is considered, by deriving the nth 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.

Suggested Citation

  • Riganti, Riccardo, 1988. "Evolution of the nth probability density and entropy function in stochastic systems," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 30(3), pages 231-242.
    • Handle: RePEc:eee:matcom:v:30:y:1988:i:3:p:231-242
    DOI: 10.1016/0378-4754(88)90002-X
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    References listed on IDEAS

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    1. Bellomo, N. & Cafaro, E. & Rizzi, G., 1984. "On the mathematical modelling of physical systems by ordinary differential stochastic equations," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 26(4), pages 361-367.
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    Cited by:

    1. Zavattaro, M.G. & Riganti, R., 1992. "Statistics of the solution of singularly perturbed systems with random initial conditions," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 34(5), pages 487-499.

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