The law of a stochastic integral with two independent fractional Brownian motions

Xavier Bardina and Ciprian Tudor

Departament de Matemàtiques, Edifici C, Universitat Autònoma de Barcelona 08193 Bellaterra, Barcelona, Spain
SAMOS/MATISSE, Université de Panthéon-Sorbonne Paris 1, 90, rue de Tolbiac, 75634 Paris Cedex 13, France.

Abstract

Using the tools of the stochastic integration with respect to the fractional Brownian motion, we obtain the expression of the characteristic function of the random variable $\int_{0}^{1}B^{\alpha }_{s}dB^{H}_{s}$ where $B^{\alpha }$ and $B^{H}$ are two independent fractional Brownian motions with Hurst parameters $\alpha\in(0,1) $ and $H>\frac12$ respectively. The two-parameter case is also considered.

Published in: Boletín de la SMM 13(1) (2007)