Central Limit Theorem in the Space of Continuous Functions in the Case of Convergence to a Stable Distribution

E. I. Ostrovskii

Obninsk Institute for Nuclear Power Engineering

Abstract: In this article we study weak convergence of distributions of normed sums of independent random fields with an arbitrary compact parametric set to a nondegenerate stable distribution in the corresponding Banach space of continuous functions. We present new entropy conditions for the parametric set which provide this convergence.

Key words: Pisier functional, entropy weak convergence, stable distribution, nonasymptotic estimate.

UDC: 519.21

Received: 28.07.1998

 English version: Siberian Advances in Mathematics, 1999, 9:3, 132–150

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