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A Hölderian FCLT for some multiparameter summation process of independent non-identically distributed random variables
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Vaidotas Zemlys, Vilnius University
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Abstract
We introduce a new construction of a summation process based on the collection
of rectangular subsets of unit d-dimensional cube for a triangular array of
independent non-identically distributed variables with d-dimensional index,
using the non-uniform grid adapted to the variances of the variables. We
investigate its convergence in distribution in some Holder spaces. It turns out
that for dimensions greater than 2, the limiting process is not necessarily
the standard Brownian sheet. This contrasts with a classical result of
Prokhorov for the one-dimensional case.
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Full text: PDF
Pages: 2259-2282
Published on: December 21, 2008
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Electronic Journal of Probability. ISSN: 1083-6489 |
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