Weak convergence of summation processes in Besov spaces

Volume 165 / 2004

Bruno Morel Studia Mathematica 165 (2004), 19-37 MSC: Primary 60F17; Secondary 46E35, 60G17. DOI: 10.4064/sm165-1-2


We prove invariance principles for partial sum processes in Besov spaces. This functional framework allows us to give a unified treatment of the step process and the smoothed process in the same parametric scale of function spaces. Our functional central limit theorems in Besov spaces hold for i.i.d. sequences and also for a large class of weakly dependent sequences.


  • Bruno MorelLaboratoire de Statistique et de Probabilités
    F.R.E. CNRS 2222
    Bât. M2, U.F.R. de Mathématiques
    Université des Sciences et Technologies de Lille
    F-59655 Villeneuve d'Ascq Cedex, France

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