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A Hölderian functional central limit theorem for a multi-indexed summation process

Author

Listed:
  • Rackauskas, Alfredas
  • Suquet, Charles
  • Zemlys, Vaidotas

Abstract

Let be an i.i.d. random field of square integrable centered random elements in the separable Hilbert space and , , be the summation processes based on the collection of sets [0,t1]x...x[0,td], 0 =2, we characterize the weak convergence of in the Hölder space by the finiteness of the weak p moment of for p=(1/2-[alpha])-1. This contrasts with the Hölderian FCLT for d=1 and [A. Rackauskas, Ch. Suquet, Necessary and sufficient condition for the Lamperti invariance principle, Theory Probab. Math. Statist. 68 (2003) 115-124] where the necessary and sufficient condition is P(X1>t)=o(t-p).

Suggested Citation

  • Rackauskas, Alfredas & Suquet, Charles & Zemlys, Vaidotas, 2007. "A Hölderian functional central limit theorem for a multi-indexed summation process," Stochastic Processes and their Applications, Elsevier, vol. 117(8), pages 1137-1164, August.
  • Handle: RePEc:eee:spapps:v:117:y:2007:i:8:p:1137-1164
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    References listed on IDEAS

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    1. Alfredas Račkauskas & Charles Suquet, 2006. "Testing Epidemic Changes of Infinite Dimensional Parameters," Statistical Inference for Stochastic Processes, Springer, vol. 9(2), pages 111-134, July.
    2. Ziegler, Klaus, 1997. "Functional Central Limit Theorems for Triangular Arrays of Function-Indexed Processes under Uniformly Integrable Entropy Conditions," Journal of Multivariate Analysis, Elsevier, vol. 62(2), pages 233-272, August.
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