Asymptotic Normality for a Vector Stochastic Difference Equation with Applications in Stochastic Approximation
AbstractIn this paper, we consider an asymptotic normality problem for a vector stochastic difference equation of the formUn+1=(I+an(B+En))Â Un+an(un+en), whereBis a stable matrix, andEn-->n0,anis a positive real step size sequence withan-->n0, [summation operator][infinity]n=1Â an=[infinity], anda-1n+1-a-1n-->n[lambda][greater-or-equal, slanted]0,unis an infinite-term moving average process, and[formula]. Obviously,anhere is a quite general step size sequence and includes (logÂ n)[beta]/n[alpha],
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Bibliographic InfoArticle provided by Elsevier in its journal Journal of Multivariate Analysis.
Volume (Year): 57 (1996)
Issue (Month): 1 (April)
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Web page: http://www.elsevier.com/wps/find/journaldescription.cws_home/622892/description#description
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- Koval, Valery & Schwabe, Rainer, 2003. "A law of the iterated logarithm for stochastic approximation procedures in d-dimensional Euclidean space," Stochastic Processes and their Applications, Elsevier, vol. 105(2), pages 299-313, June.
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