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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
DOI: https://doi.org/10.1090/S0002-9939-1972-0326812-3
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.


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DOI: https://doi.org/10.1090/S0002-9939-1972-0326812-3
Keywords: Linear stochastic process, $ {l_\varphi }$-compatible, weakly $ \varphi $-finite
Article copyright: © Copyright 1972 American Mathematical Society