Communications for Statistical Applications and Methods

The Korean Statistical Society (한국통계학회)
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A Note on a Result of Yu. V. Prokhorov in General Banach Spaces

  • Dug Hun Hong (School of Mechanical and Automotive Engineering, Catholic University of Taegu-Hyosung, Kyungbuk 712-702 Korea)
  • Published : 1997.04.01
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Abstract

We prove a conjecture of Yu. V. Prokhorov in general Banach Spaces ; let ($X_n$, n$\geq$1} be a sequence of independent identically and symmetrically distributed Banach valued random variables, then the relation $\mid$$\mid$$S_n$$\mid$$\mid$/$b_n$ -> 1 a.s. cannot hold for any choice of constants $b_n$.

Keywords

References

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  4. Theory of Probability and its Application v.31 On a conjecture of Yu. V. Prokhorov Martikainen, A.I.
  5. Theory of Probability and its Application v.28 On sums of random vectors with values in Hilbert space Prokhorov, Yu. V.