On H -Valued Continuous Robbins - Monro Processes.
Ali, H., Elnagar, H. (1998). On H -Valued Continuous Robbins - Monro Processes.. EKB Journal Management System, 42(2), 155-164. doi: 10.21608/esju.1998.314572
Hoda Mohamed Ali; Hala Elnagar. "On H -Valued Continuous Robbins - Monro Processes.". EKB Journal Management System, 42, 2, 1998, 155-164. doi: 10.21608/esju.1998.314572
Ali, H., Elnagar, H. (1998). 'On H -Valued Continuous Robbins - Monro Processes.', EKB Journal Management System, 42(2), pp. 155-164. doi: 10.21608/esju.1998.314572
Ali, H., Elnagar, H. On H -Valued Continuous Robbins - Monro Processes.. EKB Journal Management System, 1998; 42(2): 155-164. doi: 10.21608/esju.1998.314572

On H -Valued Continuous Robbins - Monro Processes.

The Egyptian Statistical Journal
Article 2, Volume 42, Issue 2, December 1998, Page 155-164  XML PDF (7.56 MB)
Document Type: Original Article
DOI: 10.21608/esju.1998.314572
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Authors
Hoda Mohamed Ali* ; Hala Elnagar
Dep.of Mathematics , Faculty of Science, (for Girls), Al-Azhar University, Egypt
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.
Keywords
Almost Sure Convergence; Continuous Robbins-Monro Process; Hilbert Space; Modified Process; Nonlinear Mapping; Stochastic Approximation Algorithms
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