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314572

On H -Valued Continuous Robbins - Monro processes.

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Last updated: 11 May 2025

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Abstract

In this work, we consider a continuous Robbins - Monro process in a Hilbert space, a nonlinear mapping ƒ is treated instead of the usual linearity assumption.  A modified process with varying truncations is analyzed, and the asymptotic properties are investigated and convergence as well as necessary and sufficient conditions are obtained. Yin and Zhu [7] considered the discrete Robbins Monro in a Hilbert space, and we extend their results to the continuous case, by introducing randomly varying truncations and we prove the almost sure convergence of the stochastic approximation algorithms.

DOI

10.21608/esju.1998.314572

Keywords

Almost Sure Convergence, Continuous Robbins-Monro Process, Hilbert space, Modified Process, Nonlinear Mapping, Stochastic Approximation Algorithms

Authors

First Name

Hoda

Last Name

Ali

MiddleName

Mohamed

Affiliation

Dep.of Mathematics , Faculty of Science, (for Girls), Al-Azhar University, Egypt

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First Name

Hala

Last Name

Elnagar

MiddleName

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Affiliation

Dep.of Mathematics , Faculty of Science, (for Girls), Al-Azhar University, Egypt

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Volume

42

Article Issue

2

Related Issue

43142

Issue Date

1998-12-01

Publish Date

1998-12-01

Page Start

155

Page End

164

Print ISSN

0542-1748

Online ISSN

2786-0086

Article File

ESJU_Volume 42_Issue 2_Pages 155-164.pdf

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Link

https://esju.journals.ekb.eg/article_314572.html

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http://journals.ekb.eg?_action=service&article_code=314572

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Original Article

Type Code

1,914

Publication Type

Journal

Publication Title

The Egyptian Statistical Journal

Publication Link

https://esju.journals.ekb.eg/

MainTitle

On H -Valued Continuous Robbins - Monro processes.

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Article

Created At

28 Dec 2024