Linear processes generated by independent random variables
HTML articles powered by AMS MathViewer
- by W. A. Woyczyński PDF
- Proc. Amer. Math. Soc. 34 (1972), 515-520 Request permission
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
-
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.
- R. M. Dudley, Random linear functionals, Trans. Amer. Math. Soc. 136 (1969), 1–24. MR 264726, DOI 10.1090/S0002-9947-1969-0264726-2
- S. Mazur and W. Orlicz, On some classes of linear spaces, Studia Math. 17 (1958), 97–119. MR 98319, DOI 10.4064/sm-17-1-97-119
- W. A. Woyczyński, Representation of additive functionals and invariant characteristic functionals of linear process with independent pieces, Bull. Acad. Polon. Sci. Sér. Sci. Math. Astronom. Phys. 19 (1971), 221–230 (English, with Russian summary). MR 292156
Additional Information
- © Copyright 1972 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 34 (1972), 515-520
- MSC: Primary 60F05
- DOI: https://doi.org/10.1090/S0002-9939-1972-0326812-3
- MathSciNet review: 0326812