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Central limit theorem and weak law of large numbers with rates for martingales in Banach spaces

Author

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  • Butzer, P. L.
  • Hahn, L.
  • Roeckerath, M. Th.

Abstract

This paper is concerned with large- error estimates concerning convergence in distribution as well as norm convergence for Banach space-valued martingale difference sequences. Indeed, two general limit theorems equipped with rates of convergence for such difference sequences are established. Applications of these lead to the central limit theorem and the weak law of large numbers with rates for Banach space-valued martingales.

Suggested Citation

  • Butzer, P. L. & Hahn, L. & Roeckerath, M. Th., 1983. "Central limit theorem and weak law of large numbers with rates for martingales in Banach spaces," Journal of Multivariate Analysis, Elsevier, vol. 13(2), pages 287-301, June.
    • Handle: RePEc:eee:jmvana:v:13:y:1983:i:2:p:287-301
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