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Contents of PMS, Vol. 19, Fasc. 1,
pages 133 - 152
 

CENTRAL LIMIT THEOREM IN HÖLDER SPACES

Alfredas Račkauskas
Charles Suquet

Abstract: Stochastic processes are considered within the framework of Hölder spaces H0
  a  as paths spaces. Using Ciesielski’s isomorphisms between H0
 a  and sequences spaces via the Faber Schauder triangular functions allows us to express our basic assumptions in terms of second differences of the processes, giving more flexibility. We obtain general conditions for the existence of a version with paths in H0
  a  and the tightness of sequences of random elements in these spaces. Central limit theorems in H0
  a  are established and convergence rates are given with respect to Prohorov and bounded Lipschitz metrics. As an application, we study the weak Holder convergence of the characteristic empirical process.

2000 AMS Mathematics Subject Classification: Primary: -; Secondary: -;

Key words and phrases: -

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