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The Hájek-Rényi inequality for Banach space valued martingales and the p smoothness of Banach spaces

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  • Shixin, Gan

Abstract

A p-smoothable Banach space is characterized in terms of the Hájek-Rényi inequality for Banach space valued martingales. As applications of this inequality, the strong law of large numbers and integrability of the supremum of Banach space valued martingales are also given.

Suggested Citation

  • Shixin, Gan, 1997. "The Hájek-Rényi inequality for Banach space valued martingales and the p smoothness of Banach spaces," Statistics & Probability Letters, Elsevier, vol. 32(3), pages 245-248, March.
    • Handle: RePEc:eee:stapro:v:32:y:1997:i:3:p:245-248
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    Citations

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    Cited by:

    1. Liu, Jingjun & Gan, Shixin & Chen, Pingyan, 1999. "The Hájeck-Rényi inequality for the NA random variables and its application," Statistics & Probability Letters, Elsevier, vol. 43(1), pages 99-105, May.
    2. Stefano Maria IACUS & Nakahiro YOSHIDA, 2009. "Estimation for the change point of the volatility in a stochastic differential equation," Departmental Working Papers 2009-49, Department of Economics, Management and Quantitative Methods at Università degli Studi di Milano.
    3. Prakasa Rao, B. L. S., 2002. "Application of Whittle's inequality for banach space valued martingales," Statistics & Probability Letters, Elsevier, vol. 57(2), pages 133-137, April.
    4. Iacus, Stefano M. & Yoshida, Nakahiro, 2012. "Estimation for the change point of volatility in a stochastic differential equation," Stochastic Processes and their Applications, Elsevier, vol. 122(3), pages 1068-1092.

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