On Random Multipliers in the Central Limit Theorem with p-stable Limit, 0 < p < 2

  • Evarist Giné
  • Michael B. Marcus
  • Joel Zinn
Part of the Progress in Probability book series (PRPR, volume 20)


Let B be a separable Banach space with dual space B*. Let X be a B-valued random variable, {X j } j=1 independent identically distributed (i.i.d.) copies of X, {ε j } j=1 a Rademacher sequence independent of {X j } j=1 , and {gj} an orthogaussian sequence independent of {X j } j=1 . It is well known ([5]) that X satisfies the central limit theorem in B if and only if εX satisfies the central limit theorem in B, i.e. if and only if the sequence
$$\{{{n}^{-1/2}}\sum\limits_{j=1}^{n}{{{\varepsilon }_{j}}}{{X}_{J}}\}_{n=1}^{\infty }$$
converges in distribution, and also if and only if ([6]) gX satisfies the central limit theorem in B, i.e.


Banach Space Central Limit Theorem Separable Banach Space Contraction Principle Triangular Array 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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Copyright information

© Birkhäuser Boston 1990

Authors and Affiliations

  • Evarist Giné
    • 1
  • Michael B. Marcus
    • 2
  • Joel Zinn
    • 1
  1. 1.Department of MathematicsTexas A & M UniversityCollege StationUSA
  2. 2.Department of MathematicsCity College, CUNYNew YorkUSA

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