Acta mathematica scientia,Series B ›› 2001, Vol. 21 ›› Issue (2): 229-236.

• Articles • Previous Articles     Next Articles

CONVERGNECE RATES IN THE LAW OF LARGE NUMBERS FOR B-VALUED RANDOM ELEMENTS

 LIANG Han-Ying, WANG Li   

  1. Department of Applied Mathematics, Tongji University, Shanghai 200092, China
  • Online:2001-04-07 Published:2001-04-07
  • Supported by:

    Supported by the Science Fund of Tongji University

Abstract:

The author discusses necessary and sufficient conditions of the complete con-vergence for sums of B-valued independent but not necessarily identically distributed r.v.′s in Banach space of type p, and obtain characterization of Banach space of type p in terms of the complete convergence. A series of classical results on iid real valued r.v.′s are extended.As application author gives the analogous results for randomly indexed sums.

Key words: Convergence rate, random element, Banach space of type p, slowly varying function

CLC Number: 

  • 60B12
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