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On the concentration phenomenon for [phi]-subgaussian random elements

Author

Listed:
  • Antonini, Rita Giuliano
  • Hu, Tien-Chung
  • Volodin, Andrei

Abstract

We study the deviation probability P{[short parallel]X[short parallel]-E[short parallel]X[short parallel]>t} where X is a [phi]-subgaussian random element taking values in the Hilbert space l2 and [phi](x) is an N-function. It is shown that the order of this deviation is exp{-[phi]*(Ct)}, where C depends on the sum of [phi]-subgaussian standard of the coordinates of the random element X and [phi]*(x) is the Young-Fenchel transform of [phi](x). An application to the classically subgaussian random variables ([phi](x)=x2/2) is given.

Suggested Citation

  • Antonini, Rita Giuliano & Hu, Tien-Chung & Volodin, Andrei, 2006. "On the concentration phenomenon for [phi]-subgaussian random elements," Statistics & Probability Letters, Elsevier, vol. 76(5), pages 465-469, March.
    • Handle: RePEc:eee:stapro:v:76:y:2006:i:5:p:465-469
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