Lévy area for Gaussian processes: A double Wiener-Itô integral approach

Albert Ferreiro-Castilla (1) , Frederic Utzet (2)

1 Centre de Recerca Matemàtica
2 UAB - Departament de Matemàtiques [Barcelona]

Let and be two independent continuous centered Gaussian processes with covariance functions and . We show that if the covariance functions are of finite -variation and -variation respectively and such that , then the Lévy area can be defined as a double Wiener-Itô integral with respect to an isonormal Gaussian process induced by and . Moreover, some properties of the characteristic function of that generalised Lévy area are studied.

Mots clés: 60G15; 60G22; 60H05; Lévy area; -variation; Fractional Brownian motion; Multiple Wiener-Itô integral; Young's inequality

Domaines: Bio-informatique [q-bio.QM]; Bio-Informatique, Biologie Systémique [q-bio.QM]

Albert Ferreiro-Castilla, Frederic Utzet. Lévy area for Gaussian processes: A double Wiener-Itô integral approach. Statistics and Probability Letters, 2011, 81 (9), pp.1380. ⟨10.1016/j.spl.2011.04.015⟩. ⟨hal-00762900⟩