Central Limit Theorem in Hölder Spaces

• Autorzy: Račkauskas A. , Suquet C.
• Języki publikacji: EN

Abstrakty

EN

Stochastic processes are considered within the framework of Hölder spaces H_α⁰ as paths spaces. Using Ciesielski's isomorphisms between H_α⁰ 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 H_α⁰ and the tightness of sequences of random elements in these spaces. Central limit theorems in H_α⁰ are established and convergence rates are given with respect to Prohorov and bounded Lipschitz metrics. As an application, we study the weak Hölder convergence of the characteristic empirical process.

Słowa kluczowe

EN

Hölder spaces; Ciesielski's isomorphisms; central limit theorems

• Wydawca: Wrocław University of Science and Technology
• Czasopismo: Probability and Mathematical Statistics
• Rocznik: 1999
• Tom: Vol. 19, Fasc. 1
• Strony: 133--152
• Opis fizyczny: Bibliogr. 22 poz.

Twórcy

autor

Račkauskas A.

• Department of Mathematics, Vilnius University, Naugarduko 24, Lt-2006 Vilnius, Lithuania

autor

Suquet C.

• Laboratoire de Statistique et Probabilités, Bât. M2, Université des Sciences et Technologies de Lille, F-59655 Villeneuve d'Ascq, Cedex, France

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