Canonical representations and convergence criteria for processes with interchangeable increments

  • Olav Kallenberg


Stochastic Process Probability Theory Mathematical Biology Convergence Criterion Canonical Representation 
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  1. 1.
    Billingsley, P.: Convergence of probability measures. New York: Wiley 1968.Google Scholar
  2. 2.
    Blum, J.R., Chernoff, H., Rosenblatt, M., Teicher, H.: Central limit theorems for interchangeable processes. Canad. J. Math.10, 222–229 (1958).Google Scholar
  3. 3.
    Bühlmann, H.: Austauschbare stochastische Variabein und ihre GrenzwertsÄtze. Univ. Calif. Publ. Statist.3, 1–35 (1960).Google Scholar
  4. 4.
    Chernoff, H., Teicher, H.: A central limit theorem for sums of interchangeable random variables. Ann. Math. Statist.29, 118–130 (1958).Google Scholar
  5. 5.
    Davidson, R.: Some arithmetic and geometry in probability theory. Ph. D. thesis. Cambridge University, 1968.Google Scholar
  6. 6.
    Feller, W.: An introduction to probability theory and its applications II, 2nd ed. New York: Wiley 1970.Google Scholar
  7. 7.
    Ferguson, T., Klass, M.: A representation of independent increment processes without Gaussian components. Ann. Math. Statist.43, 1634–1643 (1972).Google Scholar
  8. 8.
    de Finetti, B.: La prévision: ses lois logique, ses sources subjectives. Ann. Inst. Henri Poincaré7, 1–68 (1937).Google Scholar
  9. 9.
    Hagberg, J.: Approximation of the summation process obtained by sampling from a finite population. Teor. Verojatn. Primenen.18, (1973). (To appear.)Google Scholar
  10. 10.
    Hájek, J.: Limiting distributions in simple random sampling from a finite population. Magyar Tud. Akad. Mat. Kutató Int. Közl.5, 361–374 (1960).Google Scholar
  11. 11.
    Hewitt, E., Savage, L.J.: Symmetric measures on cartesian products. Trans. Amer. Math. Soc.80, 470–501 (1955).Google Scholar
  12. 12.
    Kallenberg, O.: Characterization and convergence of random measures and point processes. Z. Wahrscheinlichkeitstheorie verw. Geb.27, 9–21 (1973).Google Scholar
  13. 13.
    Kallenberg, O.: A canonical representation of symmetrically distributed random measures. In: Mathematics and Statistics. Essays in Honour of Harald Bergström, 41–48. Göteborg: Teknologtryck 1973.Google Scholar
  14. 14.
    Kallenberg, O.: Series of random processes without discontinuities of the second kind. (To appear.)Google Scholar
  15. 15.
    Kendall, D. G.: On finite and infinite sequences of exchangeable events. Studia Sci. Math. Hungar.2, 319–327 (1967).Google Scholar
  16. 16.
    Lindvall, T.: Weak convergence of probability measures and random functions in the function spaceD[0, ∞). J. Appl. Probability10, 109–121 (1973).Google Scholar
  17. 17.
    Loève, M.: Probability theory, 3rd ed. Princeton: Van Nostrand 1963.Google Scholar
  18. 18.
    Loève, M.: à l'intérieur du problème central. Publ. Inst. Statist. Univ. Paris6, 313–325 (1957).Google Scholar
  19. 19.
    Mecke, J.: Eine charakteristische Eigenschaft der doppelt stochastischen Poissonschen Prozesse. Z. Wahrscheinlichkeitstheorie verw. Gebiete11, 74–81 (1968).Google Scholar
  20. 20.
    Prokhorov, Yu.V.: Convergence of random processes and limit theorems in probability theory. Theor. Probability Appl.1, 157–214 (1956).Google Scholar
  21. 21.
    Rényi, A., Révész, P.: A study of sequences of equivalent events as special stable sequences. Publ. Math. Debrecen10, 319–325 (1963).Google Scholar
  22. 22.
    Rosén, B.: Limit theorems for sampling from a finite population. Ark. Mat.5, 383–424 (1964).Google Scholar
  23. 23.
    Skorokhod, A.V.: Limit theorems for stochastic processes with independent increments. Theor. Probability Appl.2, 138–171 (1957).Google Scholar
  24. 24.
    Wichura, M. J.: On the construction of almost uniformly convergent random variables with given weakly convergent image laws. Ann. Math. Statist.41, 284–291 (1970).Google Scholar

Copyright information

© Springer-Verlag 1973

Authors and Affiliations

  • Olav Kallenberg
    • 1
  1. 1.Department of MathematicsChalmers Institute of Technology and the University of GöteborgGöteborg 5Sweden

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