Geodesic
Central Limit Theorem in the~Space of Continuous Functions in the~Case of Convergence to a~Stable Distribution
Matematičeskie trudy, Tome 2 (1999) no. 1, pp. 140-159

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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. 
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     author = {E. I. Ostrovskii},
     title = {Central {Limit} {Theorem} in {the~Space} of {Continuous} {Functions} in {the~Case} of {Convergence} to {a~Stable} {Distribution}},
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E. I. Ostrovskii. Central Limit Theorem in the~Space of Continuous Functions in the~Case of Convergence to a~Stable Distribution. Matematičeskie trudy, Tome 2 (1999) no. 1, pp. 140-159. http://geodesic.mathdoc.fr/item/MT_1999_2_1_a4/