A Hölderian functional central limit theorem for a multi-indexed summation process

Alfredas Rackauskas, Charles Suquet and Vaidotas Zemlys

Stochastic Processes and their Applications, 2007, vol. 117, issue 8, 1137-1164

Abstract: Let be an i.i.d. random field of square integrable centered random elements in the separable Hilbert space and , , be the summation processes based on the collection of sets [0,t1]x...x[0,td], 0 =2, we characterize the weak convergence of in the Hölder space by the finiteness of the weak p moment of for p=(1/2-[alpha])-1. This contrasts with the Hölderian FCLT for d=1 and [A. Rackauskas, Ch. Suquet, Necessary and sufficient condition for the Lamperti invariance principle, Theory Probab. Math. Statist. 68 (2003) 115-124] where the necessary and sufficient condition is P(X1>t)=o(t-p).

Keywords: Brownian; sheet; Hilbert; space; valued; Brownian; sheet; Hilbert; space; Functional; central; limit; theorem; Holder; space; Invariance; principle; Summation; process (search for similar items in EconPapers)
Date: 2007
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