On the Relationship Between Some of the Ordóñez Cabrera–Volodin and the Cantrell–Rosalsky Strong Laws of Large Numbers for Banach Space Valued Summands

Autor:	Amy Cantrell, Andrew Rosalsky
Rok vydání:	2011
Předmět:	Statistics and Probability Discrete mathematics Strong law Convergence of random variables Joint probability distribution Stochastic process Law of large numbers Applied Mathematics Banach space Statistics Probability and Uncertainty Mathematics
Zdroj:	Stochastic Analysis and Applications. 29:444-451
ISSN:	1532-9356 0736-2994
Popis:	For Banach space valued random elements irrespective of their joint distributions, some strong laws of large numbers of Ordo ez Cabrera and Volodin [3] and of Cantrell and Rosalsky [2] are compared. For the main result in each article, it is shown that every strong law that can be produced using the Ordo ez Cabrera and Volodin [3] theorem can also be produced by using the Cantrell and Rosalsky [2] theorem. An example is provided wherein the hypotheses of the Cantrell and Rosalsky [2] theorem are satisfied but those of the Ordo ez Cabrera and Volodin [3] theorem are not satisfied. Apropos of other strong law results of Ordo ez Cabrera and Volodin [3] and of Cantrell and Rosalsky [2] which are in the same spirit, examples are provided showing that the results are not comparable in the sense that the hypotheses of each result do not imply the hypotheses of the other.
Databáze:	OpenAIRE
Externí odkaz:	https://explore.openaire.eu/search/publication?articleId=doi_________::2cbd74b4cb2d5c3d887fcc007ca3479c https://doi.org/10.1080/07362994.2011.548989 Zobrazit plný text záznamu