Exponential bounds in stochastic approximation procedures (Q915324)

Exponential bounds for the probability \(P\{| X_ n-\theta | \geq \epsilon \}\) for a Robbins-Monro process \(X_ n\) are constructed. In contrast to other results in this direction [\textit{J. Komlós} and \textit{P. Révész}, Z. Wahrscheinlichkeitstheorie Verw. Gebiete 25, 39-47 (1972; Zbl 0238.62043); \textit{M. Woodroofe}, ibid. 21, 329-338 (1972; Zbl 0215.255)] the authors allow weak dependence between the errors of measurement. They assume that certain coefficients of uniform strong mixing converge to zero sufficiently quick.