Anmerkungen:
Nach Informationen von SSRN wurde die ursprüngliche Fassung des Dokuments January 2002 erstellt
Beschreibung:
Let H be an infinite-dimensional real separable Hilbert space. Given an unknown mapping M : H H that can only be observed with noise, we consider two modified Robbins-Monro procedures to estimate the zero point o H of M. These procedures work in appropriate finite dimensional sub-spaces of growing dimension. Almost-sure convergence, functional central limit theorem (hence asymptotic normality), law of iterated logarithm (hence almost-sure loglog rate of convergence), and mean rate of convergence are obtained for Hilbert space-valued mix-ingale, -dependent error processes