ASYMPTOTICS OF THE CROSS-VARIATION OF YOUNG INTEGRALS WITH RESPECT TO A GENERAL SELF-SIMILAR GAUSSIAN PROCESS

doi:10.1007/s10473-020-0621-8

Acta mathematica scientia,Series B ›› 2020, Vol. 40 ›› Issue (6): 1941-1960.doi: 10.1007/s10473-020-0621-8

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ASYMPTOTICS OF THE CROSS-VARIATION OF YOUNG INTEGRALS WITH RESPECT TO A GENERAL SELF-SIMILAR GAUSSIAN PROCESS

Soukaina DOUISSI^1,2, Khalifa ES-SEBAIY³, Soufiane MOUSSATEN⁴

1. Laboratory LIBMA, Faculty Semlalia, University Cadi Ayyad, 40000 Marrakech, Morocco;
2. Department of Statistics and Probability, Michigan State University, East Lansing, MI 48824, USA;
3. Department of Mathematics, Faculty of Science, Kuwait University, Kuwait;
4. Faculty of Sciences Mohamed first University, Oujda, Morocco

Received:2019-04-23 Revised:2019-10-15 Online:2020-12-25 Published:2020-12-30
Contact: Soukaina DOUISSI,E-mail:douissi.soukaina@gmail.com E-mail:douissi.soukaina@gmail.com
Supported by:
The first author was supported by the Fulbright joint supervision program for PhD students for the academic year 2018-2019 between Cadi Ayyad University and Michigan State University.

Abstract

Abstract: We show in this work that the limit in law of the cross-variation of processes having the form of Young integral with respect to a general self-similar centered Gaussian process of order β ∈ (1/2, 3/4] is normal according to the values of β. We apply our results to two self-similar Gaussian processes:the subfractional Brownian motion and the bifractional Brownian motion.

Key words: self-similar Gaussian processes, Young integral, Breuer-Major theorem, subfractional Brownian motion, bifractional Brownian motion

CLC Number:

60F05

Soukaina DOUISSI, Khalifa ES-SEBAIY, Soufiane MOUSSATEN. ASYMPTOTICS OF THE CROSS-VARIATION OF YOUNG INTEGRALS WITH RESPECT TO A GENERAL SELF-SIMILAR GAUSSIAN PROCESS[J].Acta mathematica scientia,Series B, 2020, 40(6): 1941-1960.

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ASYMPTOTICS OF THE CROSS-VARIATION OF YOUNG INTEGRALS WITH RESPECT TO A GENERAL SELF-SIMILAR GAUSSIAN PROCESS

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