Analysis of Stochastic Systems Via Maximum Entropy Principle

  • K. Sobczyk
  • J. Trebicki
Part of the IUTAM Symposia book series (IUTAM)


The principle of maximum entropy introduced first in statistical physics and successfully applied in other fields (statistics, reliability theory, simulation etc.) has recently been developed to analyze the systems governed by stochastic differential equations (cf.[2],[3]). In this paper we extend the maximum entropy methodology to stochastic vibratory nonlinear systems.

Starting from general formulation of the system dynamics and assuming that an information about the response (solution) is available in the form of the equations for moments, the probability distribution of the stationary response is derived as a result of maximization of the entropy functional. Along with the basic scheme of the method the comparisons of the results with prediction of other known procedures is given.


Lagrange Multiplier Maximum Entropy Moment Equation Maximum Entropy Method Maximum Entropy Principle 
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Copyright information

© Springer-Verlag Berlin Heidelberg 1992

Authors and Affiliations

  • K. Sobczyk
    • 1
  • J. Trebicki
    • 1
  1. 1.Institute of Fundamental Technological ResearchPolish Academy of ScienceWarsawPoland

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