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Lindeberg

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  • Stephan Koetzer
    Hello there !! I have following problem concerning a condition of type Lindeberg: Assume we have: An(eps)=Mn^(2d) sum[z in Vn, E(Xnz^2 Ind( |Xnz| = eps /
    Message 1 of 1 , Apr 2, 2002
      Hello there !!

      I have following problem concerning a condition of type Lindeberg:

      Assume we have:

      An(eps)=Mn^(2d) sum[z in Vn, E(Xnz^2 Ind( |Xnz|>= eps / Mn^(2d) )] --> 0 (n-->oo) for all eps>0

      where Mn is a sequence of natural numbers, E means expected value, Xnz are random variables,

      Ind means indicator function.

      Now with this assumption following is true, but i cannot figure it out. I think it is rather a calculus problem than a stochastic one:

      The assumption above implies that there exists a positive, non-increasing null sequence (eps_n), n>=1 satisfying An(eps_n) / eps_n --> 0 as n --> oo.

      How can I see this and how can I construct such a sequence ?

      Every help is appreciated !!

      Stoeps



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