Martingales and the Robbins-Monro procedure in \(D[0,1]\)

DOI10.1016/0047-259X(78)90065-9zbMath0392.62066OpenAlexW2040233920MaRDI QIDQ1251880

Harro Walk

Publication date: 1978

Published in: Journal of Multivariate Analysis (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0047-259x(78)90065-9

zbMATH Keywords

MartingalesInvariance PrincipleStrong Law of Large NumbersRobBins-Monro ProcedureSkorohod TopologySpace of Real-Valued Functions

Mathematics Subject Classification ID

Strong limit theorems (60F15) Stochastic approximation (62L20) Martingales with continuous parameter (60G44) Convergence of probability measures (60B10)

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Cites Work

• Central limit theorems for C(S)-valued random variables
• The law of large numbers and the central limit theorem in Banach spaces
• The invariance principle for Banach space valued random variables
• An invariance principle for the Robbins-Monro process in a Hilbert space
• On Dvoretzky Stochastic Approximation Theorems
• Stochastic Approximation of Minima with Improved Asymptotic Speed
• Distances of Probability Measures and Random Variables
• On Asymptotic Normality in Stochastic Approximation
• On Weak Convergence of Stochastic Processes with Multidimensional Time Parameter
• On a Stochastic Approximation Method
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