A Continuous Dynamic Stochastic Approximation Procedure | ||||
| The Egyptian Statistical Journal | ||||
| Article 10, Volume 37, Issue 1, June 1993, Page 155-168 PDF (4.85 MB) | ||||
| Document Type: Original Article | ||||
| DOI: 10.21608/esju.1993.426939 | ||||
 View on SCiNiTO | ||||
| Author | ||||
| El Sayed Sorour* | ||||
| Dep. of Mathematics, Military Technical College, Kobry El-Kobba, Cairo, Egypt | ||||
| Abstract | ||||
| This paper considers the continuous Kiefer-Nolfowitz stochastic approximation procedure, where the regression function changes with time t. Let ED(t) be the unique minimum (maximum) of the regression function at a time t. Our goal is to select 0(t) such that ilx(t) - 0,t-0. co. It is assumed that 6)(t)= (91(t),...,913(0) and ei(t)=(B3,U(t)), j=1,...,P for B.(unknown) and U(t) (known) are elements of a Hilbert space H. Under general conditions we prove that lim flBi(t) - B.II<oo. If we restrict H to Rk and more t-)•co stringent conditions we prove that 11 x(t)- e(t)1k0,w.p.1 as | ||||
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