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Convergence of weighted partial sums when the limiting distribution is not necessarily Radon

Author

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  • Csörgo, Miklós
  • Norvaisa, Rimas
  • Szyszkowicz, Barbara

Abstract

Let be a non-separable Banach space of real-valued functions endowed with a weighted sup-norm. We consider partial sum processes as random functions with values in . We establish weak convergence statements for these processes via their weighted approximation in probability by an appropriate sequence of Gaussian random functions. The main result deals with convergence of distributions of certain functionals in the case when the Wiener measure is not necessarily a Radon measure on .

Suggested Citation

  • Csörgo, Miklós & Norvaisa, Rimas & Szyszkowicz, Barbara, 1999. "Convergence of weighted partial sums when the limiting distribution is not necessarily Radon," Stochastic Processes and their Applications, Elsevier, vol. 81(1), pages 81-101, May.
    • Handle: RePEc:eee:spapps:v:81:y:1999:i:1:p:81-101
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    References listed on IDEAS

    as
    1. Shao, Q. M., 1995. "Strong Approximation Theorems for Independent Random Variables and Their Applications," Journal of Multivariate Analysis, Elsevier, vol. 52(1), pages 107-130, January.
    2. Einmahl, Uwe, 1989. "Extensions of results of Komlós, Major, and Tusnády to the multivariate case," Journal of Multivariate Analysis, Elsevier, vol. 28(1), pages 20-68, January.
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