Baum-Katz-Nagaev type results for martingales

DOI10.1016/j.jmaa.2007.03.012zbMath1130.60020OpenAlexW2049536132MaRDI QIDQ2381955

Gheorghe Stoica

Publication date: 26 September 2007

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

Full work available at URL: https://doi.org/10.1016/j.jmaa.2007.03.012

zbMATH Keywords

Martingale differenceBaum-Katz-Nagaev theorem

Mathematics Subject Classification ID

Inequalities; stochastic orderings (60E15) Martingales with discrete parameter (60G42)

Related Items (24)

Complete convergence and complete moment convergence for randomly weighted sums of martingale difference sequence ⋮ Central limit theorem for linear groups ⋮ Complete convergence and complete moment convergence for weighted sums of extended negatively dependent random variables ⋮ Baum–Katz type theorems with exact threshold ⋮ Unnamed Item ⋮ Some Baum-Katz type results for \({\varphi}\)-mixing random variables with different distributions ⋮ Convergence rates in precise asymptotics for a kind of complete moment convergence ⋮ Complete convergence and complete moment convergence for martingale difference sequence ⋮ Convergence rates in the strong law of large numbers for martingale difference sequences ⋮ Complete moment convergence for randomly weighted sums of martingale differences ⋮ Complete convergence for weighted sums of extended negatively dependent random variables ⋮ The Baum-Katz theorem for bounded subsequences ⋮ The convergence of double-indexed weighted sums of martingale differences and its application ⋮ Convergence rates in the law of large numbers for arrays of martingale differences ⋮ Baum-Katz type theorems for martingale arrays ⋮ Complete convergence of weighted sums for arrays of rowwise \(\varphi \)-mixing random variables. ⋮ On complete convergence for weighted sums of martingale-difference random fields ⋮ Convergence rates in the SLLN for some classes of dependent random fields ⋮ A note on the rate of convergence in the strong law of large numbers for martingales ⋮ On the convergence rate for arrays of row-wise NOD random variables ⋮ Convergence rates in the law of large numbers for arrays of Banach valued martingale differences ⋮ Dynamic Pricing with Multiple Products and Partially Specified Demand Distribution ⋮ On the rate of convergence in the strong law of large numbers for martingales ⋮ The moment of maximum normed randomly weighted sums of martingale differences

Cites Work

• The Baum-Katz theorem for bounded subsequences
• Large deviations for martingales.
• A Combinatorial Lemma and Its Application to Probability Theory
• Convergence Rates in the Law of Large Numbers
• Some Limit Theorems for Large Deviations
• Complete Convergence and the Law of Large Numbers
• On a Theorem of Hsu and Robbins
• Remark on my Paper "On a Theorem of Hsu and Robbins"

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