On the rate of convergence of series of banach space valued random elements

DOI10.1016/S0362-546X(96)00217-9zbMath0893.60002MaRDI QIDQ4378931

Andrew Rosalsky, Joseph Max Rosenblatt

Publication date: 22 July 1998

Published in: Nonlinear Analysis: Theory, Methods & Applications (Search for Journal in Brave)

zbMATH Keywords

almost sure convergenceconvergence in probabilityreal separable Banach spacetail seriesindependent random elementsconvergent series of random elementsRademacher type Banach space

Mathematics Subject Classification ID

Limit theorems for vector-valued random variables (infinite-dimensional case) (60B12)

Related Items (6)

On the limiting behavior of tail series ⋮ On almost certain convergence of double series of random elements and the rate of convergence of tail series ⋮ On convergence of series of random variables with applications to martingale convergence and to convergence of series with orthogonal summands ⋮ Weak and TV consistency in Bayesian uncertainty quantification using disintegration ⋮ An application of the Ryll-Nardzewski-Woyczyński theorem to a uniform weak law for tail series of weighted sums of random elements in Banach spaces ⋮ On convergence of series of independent random elements in banach spaces

Cites Work

• A strong invariance theorem for the strong law of large numbers
• The speed of convergence of a martingale
• A mean convergence theorem and weak law for arrays of random elements in martingale type \(p\) Banach spaces
• On Sums Of Independen Random Vectors
• Iterated logarithm laws with random subsequences
• Iterated Logarithm laws for weighted averages
• On central limit and iterated logarithm supplements to the martingale convergence theorem
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