Independent Identically Distributed Summands

  • M. Loève
Part of the Graduate Texts in Mathematics book series (GTM, volume 45)


This chapter is devoted to study in some depth of consecutive sums S1, S2, .... of sequences of independent identically distributed sum-mands X1, X2,... with common law (X); we shorten “independent identically distributed” to iid. As usual, methods are emphasized. Methods and results took their definitive form in the third quarter of this century.


Random Walk Regular Variation Partial Attraction Random Step Standard Domain 
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. 27.
    Andersen, Sparre. On sums of symmetrically dependent random variables. Skand. Akturaetid. 36 (1953).Google Scholar
  2. 28.
    Andersen, Sparre. On the fluctuations of sums of random variables. Math. Scand. 1 (1953), 2 (1954).Google Scholar
  3. 29.
    Baxter, G. An analytic approach to finite fluctuation problems in probability. J. d’Anal. Math. 9 (1961).Google Scholar
  4. 30.
    Blackwell, D. Extension of a renewal theorem. Pac. J. Math. 3 (1953).Google Scholar
  5. 31.
    Chung, K. L. and Fuchs, W. H. J. On the distribution of values of sums of random variables. Mem. Am. Math. Soc. 6 (1951).Google Scholar
  6. 32.
    Chung, K. L. and Ornstein, D. On the recurrence of sums of random variables. Bull. Am. Math. Soc. 68 (1962).Google Scholar
  7. 33.
    Doblin, W. Sur l’ensemble de puissances d’une loi de probabilité. Studia Math. 9 (1940).Google Scholar
  8. 34.
    Gnedenko, B. V. Some theorems on the powers of distribution functions. Uchenye Zapiski Moskow Univ. Mat. 45 (1940).Google Scholar
  9. 35.
    Hewitt, E. and Savage, E. L. Symmetric measures on Cartesian products. Trans. Am. Math. Soc. (1955).Google Scholar
  10. 36.
    Katz, M. A note on the weak law of large numbers. Ann. Math. Statist. 39 (1968).Google Scholar
  11. 37.
    Owen, W. L. An estimate for E ∣S n for variables in the domain of normal attraction of a stable law of indexa, 1 < α < 2. Ann. of Prob. 1 (1973).Google Scholar
  12. 38.
    Pollaczec, F. Uber eine Aufgabe der Wahrscheilichkeitstheorie I, II. Math. Zeitsch. 32 (1930).Google Scholar
  13. 39.
    Pollaczec, F. Fonctions characteristiques de certaines répartitions définies au moyen de la notion d’ordre. Applications à la theorie des attentes. Comptes Rendus 234 (1952).Google Scholar
  14. 40.
    Polyà, G. Uber eine Aufgabe der Wahrscheinlichkeitsrechnung betreffend die Irrfahrt in Strassennetz. Math. Ann. 84 (1921).Google Scholar
  15. 41.
    Port, S. C. An elementary probability approach to fluctiation theorie. J. Math. Anal. and Appl. 6 (1963).Google Scholar
  16. 42.
    Ray, D. Stable processes with an absorbing barrier. Trans. Am. Math. Soc. 89 (1958).Google Scholar
  17. 43.
    Spitzer, F. A combinatorial lemma and its application to probability theory. Trans. Am. Math. Soc. 82 (1956).Google Scholar
  18. 44.
    Wendel, J. G. Order statistics of partial sums. Ann. Math. Statist. 31 (1960).Google Scholar

Copyright information

© Springer-Verlag Inc. 1977

Authors and Affiliations

  • M. Loève
    • 1
  1. 1.Departments of Mathematics and StatisticsUniversity of California at BerkeleyBerkeleyUSA

Personalised recommendations