UNIVERSITY
OF WROCŁAW
 
Main Page
Contents
Online First
General Information
Instructions for authors


VOLUMES
43.1 42.2 42.1 41.2 41.1 40.2 40.1
39.2 39.1 38.2 38.1 37.2 37.1 36.2
36.1 35.2 35.1 34.2 34.1 33.2 33.1
32.2 32.1 31.2 31.1 30.2 30.1 29.2
29.1 28.2 28.1 27.2 27.1 26.2 26.1
25.2 25.1 24.2 24.1 23.2 23.1 22.2
22.1 21.2 21.1 20.2 20.1 19.2 19.1
18.2 18.1 17.2 17.1 16.2 16.1 15
14.2 14.1 13.2 13.1 12.2 12.1 11.2
11.1 10.2 10.1 9.2 9.1 8 7.2
7.1 6.2 6.1 5.2 5.1 4.2 4.1
3.2 3.1 2.2 2.1 1.2 1.1
 
 
WROCŁAW UNIVERSITY
OF SCIENCE AND
TECHNOLOGY

Contents of PMS, Vol. 36, Fasc. 1,
pages 35 - 46
 

CROSS-VARIATION OF YOUNG INTEGRAL WITH RESPECT TO LONG-MEMORY FRACTIONAL BROWNIAN MOTIONS

Ivan Nourdin
Rola Zintout

Abstract: 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.

2000 AMS Mathematics Subject Classification: Primary: 60F05, 60G15, 60G22; Secondary: 60G18, 60H07.

Keywords and phrases: Fractional Brownian motion, Rosenblatt process, Young integral, Breuer–Major theorem, Taqqu’s theorem, stochastic differential equations.

Download:    Abstract    Full text   Abstract + References