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Central limit theorems and weak laws of large numbers in certain banach spaces

  • Evarist Giné
  • Joel Zinn
Article

Summary

For B a type 2 Banach lattice, we obtain a relationship between the central limit theorem in B and the weak law of large numbers (for the sum of the squares of the random vectors) in another Banach lattice B(2). We then obtain some two-sided estimates for E∥Snpwhich in lpspaces, 1≦p<∞, give n.a.s.c. for the weak law of large numbers. As a consequence of these estimates we also solve the domain of attraction problem in lp, p<2. Several examples and counterexamples are provided.

Keywords

Banach Space Stochastic Process Probability Theory Limit Theorem Random Vector 
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Copyright information

© Springer-Verlag 1983

Authors and Affiliations

  • Evarist Giné
    • 1
  • Joel Zinn
    • 2
  1. 1.Department of MathematicsLouisiana State UniversityBaton RougeUSA
  2. 2.Department of Statistics and ProbabilityMichigan State UniversityEast LansingUSA

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