TY - GEN

T1 - Stochastic approximation with exciting perturbation under dependent noises

AU - Granichin, O

PY - 2000

Y1 - 2000

N2 - A stochastic approximation problem is considered in the situation when the unknown regression function is measured not at the previous estimate but,; at its, slightly excited position. Errors of measurement are allowed to be either nonrandom or random with an arbitrary kind of dependence, and the zero-mean conditions is not imposed. Two estimation algorithms for estimate the root and the minimum point of regression function with projection is proposed. It is shown that the sequence of estimates {x(n)} obtained converges to the true value theta as sure and in the mean square sense. Sequence of estimates has asymptotic normality distribution when we can propose some more about errors of measurement.

AB - A stochastic approximation problem is considered in the situation when the unknown regression function is measured not at the previous estimate but,; at its, slightly excited position. Errors of measurement are allowed to be either nonrandom or random with an arbitrary kind of dependence, and the zero-mean conditions is not imposed. Two estimation algorithms for estimate the root and the minimum point of regression function with projection is proposed. It is shown that the sequence of estimates {x(n)} obtained converges to the true value theta as sure and in the mean square sense. Sequence of estimates has asymptotic normality distribution when we can propose some more about errors of measurement.

KW - stochastic approximation

KW - exciting perturbation

KW - consistency estimates

KW - regression function

KW - conditional mean value

M3 - статья в сборнике материалов конференции

SN - 0-7803-6434-1

SP - 146

EP - 149

BT - CONTROL OF OSCILLATIONS AND CHAOS, VOLS 1-3, PROCEEDINGS

A2 - Chernousko, FL

A2 - Fradkov, AL

PB - IEEE Canada

Y2 - 5 July 2000 through 7 July 2000

ER -