Abstract stochastic approximations and applications

Adam Shwartz and Nadav Berman

Stochastic Processes and their Applications, 1989, vol. 31, issue 1, 133-149

Abstract: Results on the convergence with probability one of stochastic approximation algorithms of the form [theta]n+1 = [theta]n - [gamma]n+1 h([theta]n) + un+1 are given, where the [theta]'s belong to some Banach space and {un} is a stochastic process. Using this extension of results of Kushner and Clark [10], conditions are given for the convergence of the linear algorithm . Several applications of the linear algorithm to problems of identification of (possibly distributed) systems and optimization are given. The applicability of these conditions is demonstrated via an example. The systems considered here are more general than those considered by Kushner and Shwartz [12].

Keywords: stochastic; approximation; in; Banach; space; strong; convergence; linear; algorithms (search for similar items in EconPapers)
Date: 1989
References: Add references at CitEc
Citations: View citations in EconPapers (4)

Downloads: (external link)
http://www.sciencedirect.com/science/article/pii/0304-4149(89)90107-5
Full text for ScienceDirect subscribers only

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:eee:spapps:v:31:y:1989:i:1:p:133-149

Ordering information: This journal article can be ordered from
http://http://www.elsevier.com/wps/find/supportfaq.cws_home/regional
https://shop.elsevie ... _01_ooc_1&version=01

Access Statistics for this article

Stochastic Processes and their Applications is currently edited by T. Mikosch

More articles in Stochastic Processes and their Applications from Elsevier
Bibliographic data for series maintained by Catherine Liu ().