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


  • Zhu, Yunmin


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],

Suggested Citation

  • Zhu, Yunmin, 1996. "Asymptotic Normality for a Vector Stochastic Difference Equation with Applications in Stochastic Approximation," Journal of Multivariate Analysis, Elsevier, vol. 57(1), pages 101-118, April.
  • Handle: RePEc:eee:jmvana:v:57:y:1996:i:1:p:101-118

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    Cited by:

    1. Pelletier, Mariane, 1999. "An Almost Sure Central Limit Theorem for Stochastic Approximation Algorithms," Journal of Multivariate Analysis, Elsevier, vol. 71(1), pages 76-93, October.
    2. 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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