On the Toeplitz Lemma, Convergence in Probability, and Mean Convergence

DOI10.1080/07362994.2013.799406zbMath1273.60029OpenAlexW2007869489WikidataQ124948831 ScholiaQ124948831MaRDI QIDQ2844035

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Publication date: 27 August 2013

Published in: Stochastic Analysis and Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1080/07362994.2013.799406

zbMATH Keywords

almost sure convergencemoment generating functioncontinuity theoremconvergence in probabilitymean convergenceKronecker lemmaToeplitz lemmaCesàro mean convergence theorem

Mathematics Subject Classification ID

Central limit and other weak theorems (60F05) Strong limit theorems (60F15) Convergence and divergence of series and sequences (40A05) (L^p)-limit theorems (60F25)

Related Items (5)

Toeplitz lemma in geodesic metric space and convergence of inductive means ⋮ Central limit theorem for linear processes generated by m-dependent random variables under the sub-linear expectation ⋮ Synchronization of reinforced stochastic processes with a network-based interaction ⋮ Toeplitz lemma, complete convergence, and complete moment convergence ⋮ Central limit theorem for linear processes generated by IID random variables under the sub-linear expectation

Cites Work

• Stochastic convergence of weighted sums of random elements in linear spaces
• On the subspaces of \(L^p\) \((p > 2)\) spanned by sequences of independent random variables
• Inequalities for the $r$th Absolute Moment of a Sum of Random Variables, $1 \leqq r \leqq 2$
• A Note on the Theory of Moment Generating Functions
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