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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)



Linear processes generated by independent random variables

Author: W. A. Woyczyński
Journal: Proc. Amer. Math. Soc. 34 (1972), 515-520
MSC: Primary 60F05
MathSciNet review: 0326812
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Abstract: In a recent paper R. Dudley gave a characterization of those sequences of independent and identically distributed random variables which are $ {l_p}$-compatible for $ p \geqq 1$. In the present note we extend his result into $ p \in (0,1]$ and provide some conditions (necessary or sufficient) for $ {l_\varphi }$-compatibility of a sequence of independent random variables not necessarily identically distributed.

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

  • [1] A. Badrikian, Séminaire sur les mesures cylindriques et les fonctions linéaires aléatoires, Lecture Notes in Math., no. 139, Springer-Verlag, Berlin and New York, 1970.
  • [2] R. M. Dudley, Random linear functionals, Trans. Amer. Math. Soc. 136 (1969), 1-24. MR 41 #9317. MR 0264726 (41:9317)
  • [3] S. Mazur, and W. Orlicz, On some classes of linear spaces, Studia Math. 17 (1958), 97-119. MR 20 #4780. MR 0098319 (20:4780)
  • [4] W. A. Woyczyński, Representation of additive functionals and invariant characteristic functionals of linear processes-with independent pieces, Bull. Acad. Polon. Sci. Ser. Sci. Math. Astronom. Phys. 19 (1971), 221-230. MR 0292156 (45:1243)

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Keywords: Linear stochastic process, $ {l_\varphi }$-compatible, weakly $ \varphi $-finite
Article copyright: © Copyright 1972 American Mathematical Society

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