Cross-variation of Young integral with respect to long-memory fractional Brownian motions35

  1. Ivan Nourdin
  2. 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.

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Probability and Mathematical Statistics

36, z. 1, 2016

Pages from 35 to 46

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