Asymptotic Normality for a Vector Stochastic Difference Equation with Applications in Stochastic Approximation

Yunmin Zhu

Journal of Multivariate Analysis, 1996, vol. 57, issue 1, 101-118

Abstract: In this paper, we consider an asymptotic normality problem for a vector stochastic difference equation of the formUn+1=(I+an(B+En)) Un+an(un+en), whereBis a stable matrix, andEn-->n0,anis a positive real step size sequence withan-->n0, [summation operator][infinity]n=1 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 (log n)[beta]/n[alpha],

Keywords: asymptotic; normality; stochastic; difference; equation; stochastic; approximation; (null) (search for similar items in EconPapers)
Date: 1996
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