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

Florian Hechner () and Bernard Heinkel ()
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Florian Hechner: Université de Strasbourg
Bernard Heinkel: Université de Strasbourg

Journal of Theoretical Probability, 2010, vol. 23, issue 2, 509-522

Abstract: Abstract 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.

Keywords: Marcinkiewicz–Zygmund law of large numbers; Banach spaces; Amart; Quasimartingale; Type of a Banach space; 60B12; 60G48; 60F15 (search for similar items in EconPapers)
Date: 2010
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Citations: View citations in EconPapers (4)

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DOI: 10.1007/s10959-009-0212-z

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