On H-valued Robbins-Monro processes

DOI10.1016/0047-259X(90)90064-OzbMath0702.62076MaRDI QIDQ915322

G. George Yin, Yunmin Zhu

Publication date: 1990

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

zbMATH Keywords

rate of convergenceasymptotic propertiesHilbert spacenecessary and sufficient conditionsnonlinear mappingRobbins-Monro processesvarying truncation

Mathematics Subject Classification ID

Strong limit theorems (60F15) Stochastic approximation (62L20) Limit theorems for vector-valued random variables (infinite-dimensional case) (60B12)

Related Items (12)

Relative entropy minimization over Hilbert spaces via Robbins-Monro ⋮ Algorithms for Kullback--Leibler Approximation of Probability Measures in Infinite Dimensions ⋮ On the use of stochastic approximation in recursive estimation ⋮ On h–valued stochastic approximation: finite dimenstional projections ⋮ An iteratively regularized stochastic gradient method for estimating a random parameter in a stochastic PDE. A variational inequality approach ⋮ Partial least squares for functional joint models with applications to the Alzheimer's disease neuroimaging initiative study ⋮ Uncertainty Quantification for Stochastic Approximation Limits Using Chaos Expansion ⋮ A variational inequality based stochastic approximation for inverse problems in stochastic partial differential equations ⋮ Stochastic proximal gradient methods for nonconvex problems in Hilbert spaces ⋮ Projected Stochastic Gradients for Convex Constrained Problems in Hilbert Spaces ⋮ Rate of convergence of stochastic approximation procedures in a Banach space ⋮ A regularized stochastic subgradient projection method for an optimal control problem in a stochastic partial differential equation

Cites Work

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• Convergence and robustness of the Robbins-Monro algorithm truncated at randomly varying bounds
• Abstract stochastic approximations and applications
• A stopping rule for the Robbins-Monro method
• Asymptotic Properties of Stochastic Approximations with Constant Coefficients
• An invariance principle for the Robbins-Monro process in a Hilbert space
• On the rate of convergence of the Robbins-Monro method

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