Cross-variation of Young integral with respect to long-memory fractional Brownian motions

• Autorzy: Nourdin I. , Zintout R.
• Języki publikacji: EN

Abstrakty

EN

We study the asymptotic behaviour of the cross-variation of two-dimensional processes having the form of a Young integral with respect to a fractional Brownian motion of index H > 1/2 . When H is smaller than or equal to 3/4 , we show asymptotic mixed normality. When H is stricly greater than 3/4 , we obtain a limit that is expressed in terms of the difference of two independent Rosenblatt processes.

Słowa kluczowe

EN

fractional Brownian motion; Rosenblatt process; Young integral; Breuer-Major theorem; Taqqu’s theorem; stochastic differential equations

• Wydawca: Wrocław University of Science and Technology
• Czasopismo: Probability and Mathematical Statistics
• Rocznik: 2016
• Tom: Vol. 36, Fasc. 1
• Strony: 35--46
• Opis fizyczny: Bibliogr. 16 poz.

Twórcy

autor

Nourdin I.

• Faculté des Sciences, de la Technologie, et de la Communication, UR en Mathématiques, Université de Luxembourg, 6 rue Richard Coudenhove-Kalergi, L-1359 Luxembourg

autor

Zintout R.

• Institut Elie Cartan, UMR 7502, Nancy Université – CNRS – INRIA, Campus Aiguillettes, B.P. 70239, F-54506, Vandoeuvre-lès-Nancy, France

Bibliografia

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• [13] M. S. Taqqu,Weak convergence to fractional Brownian motion and to the Rosenblatt process, Z. Wahrsch. Verw. Gebiete 31 (1975), pp. 287-302.
• [14] M. S. Taqqu, The Rosenblatt process, in: Selected Works of Murray Rosenblatt, R. A. Davis, K.-S. Lii, and D. N. Politis (Eds.), Sel. Works Probab. Stat., 2011, pp. 29-45.
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Uwagi

Opracowanie rekordu w ramach umowy 509/P-DUN/2018 ze środków MNiSW przeznaczonych na działalność upowszechniającą naukę (2019).