aequationes mathematicae

, Volume 2, Issue 2–3, pp 137–143 | Cite as

Non-negative definite solutions of certain differential and functional equations

  • Eugene Lukacs
Expository Papers
Received:

Keywords

Functional Equation Definite Solution 
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.
This is a preview of subscription content, log in to check access.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. [1]
    Gnedenko, B. V. andKolmogorov, A. N.,Limit Distributions for Sums of Independent Random Variables (Addison-Wesley, Cambridge, Mass. 1954).Google Scholar
  2. [2]
    Laha, R. G. andLukacs, E.,On Linear Forms Whose Distribution is Identical with that of a Monomial, Pacific J. Math.15, 207–214, (1965).Google Scholar
  3. [3]
    Laha, R. G. andLukacs, E.,On a Characterization of the Wiener Process, inTrans. of the Second Prague Conference (1960), pp. 307–312.Google Scholar
  4. [4]
    Laha, R. G. andLukacs, E.,On Identically Distributed Stochastic Integrals, inTrans. of the Third Prague Conference (1964), pp. 467–474.Google Scholar
  5. [5]
    Laha, R. G. andLukacs, E.,On Linear Forms and Stochastic Integrals, inProc. 35th Session of the International Statistical Institute, Belgrade, Vol. 2 (1965), pp. 828–840.Google Scholar
  6. [6]
    Linnik, Yu. V.,Linear Forms and Statistical Criteria, I, II (Russ.), Ukrain Math. Ž.5, 207–243, 247–290(1953), —Selected Transl. in Math. Stat. and Probab., Amer. Math. Soc.3, 1–90 (1962).Google Scholar
  7. [7]
    Linnik, Yu. V.,On Polynomical Statistics in Connection with the Analytical Theory of Differential Equations (Russ.), Vestnik Leningrad Univ.11, 35–48 (1956). =Selected Transl. in Math. Stat. and Probab., Amer. Math. Soc.1 191–206 (1961).Google Scholar
  8. [8]
    Lukacs, E. andLaha, R. G.,Applications of Characteristic Functions (Charles Griffin, London 1964).Google Scholar
  9. [9]
    Lukacs, E.,Some Results in the Theory of the Wiener Integral, inTrans. of the Fourth Prague Conference (1967), pp. 29–43.Google Scholar
  10. [10]
    Lukacs, E.,Une caractérisation des processus stables et symétriques, C. R. Acad. Sci. Paris264, 959–960 (1967).Google Scholar
  11. [11]
    Lukacs, E. On the Characterization of a Family of Popalations Which Includes Poisson Populations, Ann. Univ. Sci. Budapest. Eötvös Sect. Math.3–4, 159–175 (1960–1961).Google Scholar
  12. [12]
    Lukacs, E.,Some Extensions of a Theorem of Marcinkiewicz, Pacific J. Math.8, 487–501 (1958).Google Scholar
  13. [13]
    Marcinkiewicz, J. Sur une propriété de la loi de Gauss Math. Z.44, 612–618 (1939), also inCollected Papers (P.W.N., Warszawa 1964), pp. 463–469.Google Scholar
  14. [14]
    Raikov, D. A. On the Decomposition of Gauss and Poisson Laws, Izv. Akad. Nauk SSSR Ser. Mat.2, 91–124 (1938).Google Scholar
  15. [15]
    Zinger, A.A. andLinnik, Yu. V.,On a Class of Differential Equations with Applications to Certain Questions of Regression Theory (Russ.), Vestnik Leningrad Univ.12, 121–130 (1957). =Selected Transl. in Math. Stat. and Probab. Amer. Math. Soc.3, 181–190 (1962).Google Scholar

Copyright information

© Birkhäuser Verlag 1968

Authors and Affiliations

  • Eugene Lukacs
    • 1
  1. 1.The Catholic University of AmericaWashington, D.C.USA

Personalised recommendations