The Marcinkiewicz–Zygmund LLN in Banach Spaces: A Generalized Martingale Approach.

Autor: Hechner, Florian, Heinkel, Bernard
Zdroj: Journal of Theoretical Probability; Jun2010, Vol. 23 Issue 2, p509-522, 14p
Abstrakt: A result due to Gut asserts that the Marcinkiewicz–Zygmund strong law of large numbers for real-valued random variables is an amart a.s. convergence property. In this paper, a necessary and sufficient condition is given, under which that SLLN is also a quasimartingale. We also study the case of Banach-space valued r.v. and show that the scalar result remains true when the space is of suitable stable type. [ABSTRACT FROM AUTHOR]
Databáze: Complementary Index