Hiroshima Mathematical Journal

On a functional of distribution functions having maximum at Gaussian distribution function

Hiroshi Murata

Full-text: Open access

Article information

Source
Hiroshima Math. J., Volume 9, Number 2 (1979), 547-554.

Dates
First available in Project Euclid: 21 March 2008

Permanent link to this document
https://projecteuclid.org/euclid.hmj/1206134900

Digital Object Identifier
doi:10.32917/hmj/1206134900

Mathematical Reviews number (MathSciNet)
MR535526

Zentralblatt MATH identifier
0437.60011

Subjects
Primary: 60E05: Distributions: general theory
Secondary: 80A10: Classical thermodynamics, including relativistic

Citation

Murata, Hiroshi. On a functional of distribution functions having maximum at Gaussian distribution function. Hiroshima Math. J. 9 (1979), no. 2, 547--554. doi:10.32917/hmj/1206134900. https://projecteuclid.org/euclid.hmj/1206134900


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References

  • [1] W. Feller, An Introduction to Probability Theory and Its Applications Vol. 1, 3rd ed., John Wiley and Sons, Inc., New York London Sydney.
  • [2] R. Kond and A. Negoro, Certain functional of probability measures on Hubert spaces, Hiroshima Math. J., 6 (1976), 421-428.
  • [3] H. P. McKean, Entropy is the only increasing functional of Kac's one-dimensional caricature of a Maxwellian gas, Z. Wahrscheinlichkeitstheorie verw. Geb., 2 (1963), 167-172.
  • [4] H. Murata, Propagation of chaos for Boltzmann-like equation of non-cutoff type in the plane, Hiroshima Math. J., 7 (1977), 479-515.
  • [5] H. Murata and H. Tanaka, An inequality for certain functional of multidimensional probability distributions, Hiroshima Math. J., 4 (1974), 75-81.
  • [6] H. Tanaka, An inequality for a functional of probability distributions and its application to Kac's one-dimensional model of a Maxwellian gas, Z. Wahrscheinlichkeitstheorie verw. Geb., 27 (1973), 47-52.