Necessary and Sufficient Condition for the Functional Central Limit Theorem in Hölder Spaces

Alfredas Račkauskas () and Charles Suquet ()
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Alfredas Račkauskas: Vilnius University
Charles Suquet: Université Lille I

Journal of Theoretical Probability, 2004, vol. 17, issue 1, 221-243

Abstract: Abstract Let (X i ) i≥1 be an i.i.d. sequence of random elements in the Banach space B, S n ≔X 1+⋅⋅⋅+X n and ξ n be the random polygonal line with vertices (k/n,S k ), k=0,1,...,n. Put ρ(h)=h α L(1/h), 0≤h≤1 with 0 t)=o(t −p(α)) where p(α)=1/(1/2−α). This completes Lamperti (1962) invariance principle.

Keywords: Central limit theorem in Banach spaces; Hölder space; invariance principle; partial sums process (search for similar items in EconPapers)
Date: 2004
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DOI: 10.1023/B:JOTP.0000020482.66224.6c

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