ISSN:
1572-9036
Keywords:
60F05
;
60F17
;
62L20
;
Stochastic approximation
;
Brownian motion
;
asymptotic optimality
;
asymptotic normality
Source:
Springer Online Journal Archives 1860-2000
Topics:
Mathematics
Notes:
Abstract This paper is concerned with a continuous time stochastic approximation/optimization problem. The algorithm is given by a pair of differential-integral equations. Our main effort is to derive the asymptotic properties of the algorithm. It is shown that ast → ∞, a suitably normalized sequence of the estimation error,Τ√t(¯x tr−θ) is equivalent to a scaled sequence of the random noise process, namely, (1/√t)∫ 0 tr ξsds. Consequently, the asymptotic normality is obtained via a functional invariance theorem, and the asymptotic covariance matrix is shown to be the optimal one. As a result, the algorithm is asymptotically efficient.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1007/BF00995492
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