Chinese Quarterly Journal of Mathematics ›› 2010, Vol. 25 ›› Issue (3): 464-469.

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Hàjek-Rèniy Type Inequality for Banach Space Valued Martingales and Its Applications

  

  1. Key Laboratory of Numerical Simulation of Sichuan Province, Neijiang Normal University College of Mathematics and Information Science, Neijiang Normal University
  • Received:2008-06-04 Online:2010-09-30 Published:2023-05-30
  • About author: GONG Xiao-bing(1975- ), male, native of Linshui, Sichuan, an associate professor of Neijiang Normal University, M.S.D., engages in Banach space theory and martingale theory.
  • Supported by:
     Supported by the Youth Foundation of the Department of Education of Sichuan Province(07ZB042); Supported by Natural Science Foundation of the Department of Education of Sichuan Province(09ZC071);

Abstract: In this paper, we establish the Hàjek-Rèniy type inequality for Banach space valued martingales generalizing the recent results of Tómcs and L’ibor [1]. Then p-uniformly smoothable Banach space is characterized in terms of the Hàjek-Rèniy type inequality for Banach space valued martingales. Those results generalize the recent results of Gan Shixin [2].

Key words: B-valued martingale, p-uniformly smoothable Banach space, Hàjek-Rèniy type
inequality for B-valued martingale

CLC Number: