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ON ALMOST SURE CONVERGENCE OF WEIGHTED SUMS OF RANDOM ELEMENT SEQUENCES
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作者 甘师信 《Acta Mathematica Scientia》 SCIE CSCD 2010年第4期1021-1028,共8页
We mainly study the almost sure limiting behavior of weighted sums of the form ∑ni=1 aiXi/bn , where {Xn, n ≥ 1} is an arbitrary Banach space valued random element sequence or Banach space valued martingale differen... We mainly study the almost sure limiting behavior of weighted sums of the form ∑ni=1 aiXi/bn , where {Xn, n ≥ 1} is an arbitrary Banach space valued random element sequence or Banach space valued martingale difference sequence and {an, n ≥ 1} and {bn,n ≥ 1} are two sequences of positive constants. Some new strong laws of large numbers for such weighted sums are proved under mild conditions. 展开更多
关键词 Strong law of large number almost sure convergence lp convergence weighted sums Banach space valued random element sequence Banach space martingale difference sequence
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ON THE RATE OF WEIGHTED L_p CONVERGENCE BY THE GRNWALD INTERPOLATORY OPERATORS
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作者 YaoKui ChenZhixiang 《Analysis in Theory and Applications》 2003年第2期115-120,共6页
This paper gives the weighted Lp convergence rate estimations of the Grunwald interpolatory polynomials based on the zeros of Chebyshev polynomials of the first kind, and proves that the order of the estimations is op... This paper gives the weighted Lp convergence rate estimations of the Grunwald interpolatory polynomials based on the zeros of Chebyshev polynomials of the first kind, and proves that the order of the estimations is optimal for p≥1. 展开更多
关键词 Chebyshev polynomials Grunwald interpolatory polynomials weighted lp convergence
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