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Niveau: Supérieur, Master, Bac+5

March 15, 2010 10:46 WSPC/INSTRUCTION FILE OfBm-sd-rev Operator fractional Brownian motion as limit of polygonal lines processes in Hilbert space? ALFREDAS RA?KAUSKAS Department of Mathematics and Informatics, Vilnius University, Naugarduko 24, LT-2006 Vilnius, Lithuania. Institute of Mathematics and Informatics, Akadem?os str. 4, LT-08663, Vilnius, Lithuania. CHARLES SUQUET Laboratoire P. Painlevé, UMR 8524 CNRS Université Lille I, Bât M2, Cité Scientifique, F-59655 Villeneuve d'Ascq Cedex, France. In this paper we study long memory phenomenon of functional time series. We consider an operator fractional Brownian motion with values in a Hilbert space defined via oper- ator valued Hurst coefficient. We prove that this process is a limiting one for polygonal lines constructed from partial sums of time series having space varying long memory. Keywords: Fractional Brownian motion; Hilbert space; functional central limit theorem; long memory; linear processes. Mathematics Subject Classifications (2000): 60F17; 60B12. 1. Introduction Long memory phenomenon have played an important role since the 50's when dis- covered by Hurst in certain hydrologycal data sets. Historically this paradigm has been associated with slow decay of long-lag autocorrelation of a stochastic process and certain type of scaling properties embodied in a concept of self-similarity.

March 15, 2010 10:46 WSPC/INSTRUCTION FILE OfBm-sd-rev Operator fractional Brownian motion as limit of polygonal lines processes in Hilbert space? ALFREDAS RA?KAUSKAS Department of Mathematics and Informatics, Vilnius University, Naugarduko 24, LT-2006 Vilnius, Lithuania. Institute of Mathematics and Informatics, Akadem?os str. 4, LT-08663, Vilnius, Lithuania. CHARLES SUQUET Laboratoire P. Painlevé, UMR 8524 CNRS Université Lille I, Bât M2, Cité Scientifique, F-59655 Villeneuve d'Ascq Cedex, France. In this paper we study long memory phenomenon of functional time series. We consider an operator fractional Brownian motion with values in a Hilbert space defined via oper- ator valued Hurst coefficient. We prove that this process is a limiting one for polygonal lines constructed from partial sums of time series having space varying long memory. Keywords: Fractional Brownian motion; Hilbert space; functional central limit theorem; long memory; linear processes. Mathematics Subject Classifications (2000): 60F17; 60B12. 1. Introduction Long memory phenomenon have played an important role since the 50's when dis- covered by Hurst in certain hydrologycal data sets. Historically this paradigm has been associated with slow decay of long-lag autocorrelation of a stochastic process and certain type of scaling properties embodied in a concept of self-similarity.

- operator fractional
- defined via oper- ator valued
- mean zero
- self- adjoint operator

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Language | English |

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