Remote Access Transactions of the American Mathematical Society
Green Open Access

Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 
 

 

Sign-invariant random variables and stochastic processes with sign-invariant increments


Author: Simeon M. Berman
Journal: Trans. Amer. Math. Soc. 119 (1965), 216-243
MSC: Primary 60.40
DOI: https://doi.org/10.1090/S0002-9947-1965-0185651-8
MathSciNet review: 0185651
Full-text PDF

References | Similar Articles | Additional Information

References [Enhancements On Off] (What's this?)

  • [1] S.M. Berman, An extension of the arc sine law, Ann. Math. Statist. 33 (1962), 681-684. MR 0138123 (25:1570)
  • [2] -, Oscillation of sample functions in diffusion processes, Z. Wahrscheinlichkeitstheorie und Verw. Gebiete 1 (1963), 247-250. MR 0157408 (28:642)
  • [3] R.M. Blumenthal and R.K. Getoor, Sample functions of stochastic processes with stationary independent increments, J. Math. Mech. 10 (1961), 493-516. MR 0123362 (23:A689)
  • [4] R. Cogburn and H.G. Tucker, A limit theorem for a function of the increments of a decomposable process, Trans. Amer. Math. Soc. 99 (1961), 278-284. MR 0123353 (23:A681)
  • [5] J.L. Doob, Stochastic processes, Wiley, New York, 1953. MR 0058896 (15:445b)
  • [6] P. Lévy, Sur les intégrales dont les éléments sont des variables aléatoires indépendantes, Ann. Scuola Norm. Sup. Pisa 3 (1934), 337-366.
  • [7] -, Théorie de l'addition des variables aléatoires, Gauthier-Villars, Paris, 1937.
  • [8] -, Le mouvement Brownien plan, Amer. J. Math. 62 (1940), 487-550. MR 0002734 (2:107g)
  • [9] M. Loève, Probability theory, 2nd ed., Van Nostrand, New York, 1960. MR 0123342 (23:A670)
  • [10] H. Rademacher, Einige Sätze über Reihen von allgemeinen Orthogonalfunktionen, Math. Ann. 87 (1922), 112-138. MR 1512104
  • [11] H. Steinhaus, Les probabilités denombrables et leurs rapport à la théorie de la mesure, Fund. Math. 4 (1922), 286-310.

Similar Articles

Retrieve articles in Transactions of the American Mathematical Society with MSC: 60.40

Retrieve articles in all journals with MSC: 60.40


Additional Information

DOI: https://doi.org/10.1090/S0002-9947-1965-0185651-8
Article copyright: © Copyright 1965 American Mathematical Society

American Mathematical Society