Non-Stationary Response of Stochastic Systems via Maximum Entropy Principle

  • K. Sobczyk
  • J. Trębicki
Conference paper
Part of the Solid Mechanics and its Applications book series (SMIA, volume 47)


The principle of maximum entropy states that of all distributions (probability densities) that satisfy the appropriate moment constraints one should choose the distribution having the largest informational (Shannon) entropy. Since the entropy characterizes a global randomness of a random quantity in question, the principle of maximum entropy means that the maximum entropy distribution is maximally noncommittal with regard to the missing information. Due to this reason in statistics the maximum entropy distributions have been proposed to serve as the most unbiased prior distributions in Bayesian inferences. The principle has also been successfully applied in many other fields including reliability estimation of randomly vibrating systems. However, in all these studies the prior information was presented in the form of given (constant) moments.


Maximum Entropy Stochastic System Moment Equation Maximum Entropy Method Maximum Entropy Principle 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. Ahiezer, N.I. and Krein, M.G. (1962) Some Questions in the Theory of Moments, Amer. Math. Soc., ProvidenceGoogle Scholar
  2. Frontini, M. and Tagliani, A (1994) Maximum entropy in the finite Stielties and Hamburger moment problem, J. Math. Phys. 12(35).Google Scholar
  3. Ingarden, R.S. (1963) Information theory and variational principles in statistical theories, Bull. Acad. Polo.., Ser. Math. Astr. Phys. 11, 541-547.MathSciNetzbMATHGoogle Scholar
  4. Jaynes, E. T. (1957) Information theoiy and statistical mechanics, Physical Review, 106, 620-630MathSciNetCrossRefGoogle Scholar
  5. Lin, Y. K. (1970) First-excursion failure of randomly excited structures, P. II, AIAA Jouranl 10(8), 1888-1890Google Scholar
  6. Spencer, B.F. and Bergman, L.A (1986) On the estimation of failure probability having prescribed moments of first passage time, Prob. Eng. Mech. 3(1)Google Scholar
  7. Sobczyk, K. (1991) Stochastic Differential Equations with Applications to Physics and Engineering, Kluwer Acad. Publ., Dordrecht, BostonzbMATHGoogle Scholar
  8. Sobczyk, K. and Trębicki, J. (1990) Maximum entropy principle in stochastic dynamics, Prob. Eng. Mech. 3(5)Google Scholar
  9. Sobczyk, K. and Trębicki, J. (1993) Maximum entropy principle and non-linear stochastic oscillators, Physica A 193, 448-468zbMATHCrossRefGoogle Scholar
  10. Trębicki, J. and Sobczyk, K. (1995) Maximum entropy principle and non-stationary distributions of stochastic systems. Prob. Eng. Mech, (submitted for publication)Google Scholar

Copyright information

© Kluwer Academic Publishers 1996

Authors and Affiliations

  • K. Sobczyk
    • 1
  • J. Trębicki
    • 1
  1. 1.Polish Academy of SciencesCenter of Mechanics, Institute of Fundamental Technological ResearchWarsawPoland

Personalised recommendations