On the Strong Law of Large Numbers for Weighted Sums of Random Elements in Banach Space

• Published in: Stochastic analysis and applications Vol. 21; no. 6; pp. 1305 - 1331
• Main Authors: Kuczmaszewska, Anna, Szynal, Dominik
• Format: Journal Article
• Language: English
• Published: Philadelphia, PA Taylor & Francis Group 11-01-2003; Taylor & Francis
• Subjects: Exact sciences and technology; Mathematics; Probability and statistics; Probability theory and stochastic processes; Probability theory on algebraic and topological structures; Sciences and techniques of general use; Stochastic processes; Random element; Sufficient condition; Separable space; Probability theory; Independence; Law of large numbers; Martingale; Bernoulli number; Weighted sum; Banach space; Strong solution; Convergence
• ISSN: 0736-2994; 1532-9356
• DOI: 10.1081/SAP-120026108

In this paper we present some results for the general strong law of large numbers. We consider the normed weighted sums of random elements in real separable Banach space with random and nonrandom weights. The sufficient conditions presented in the paper are formulated in terms of Chung-Teicher type conditions (cf. Chow and Teicher, Probability Theory, Independence, Interchangeability, Martingales; Springer-Verlag: New York, 1978, Teicher, Some new conditions for the strong law. Proc. Nat. Acad. Sci. USA 1968, 59 (3), 705-707.)