Rough Volterra equations 1: the algebraic integration setting

Aurélien Deya (1) , Samy Tindel (1)

1 IECN - Institut Élie Cartan de Nancy

We define and solve Volterra equations driven by an irregular signal, by means of a variant of the rough path theory called algebraic integration. In the Young case, that is for a driving signal with Hölder exponent greater than 1/2, we obtain a global solution, and are able to handle the case of a singular Volterra coefficient. In case of a driving signal with Hölder exponent in (1/3,1/2], we get a local existence and uniqueness theorem. The results are easily applied to the fractional Brownian motion with Hurst coefficient H>1/3.

Mots clés: Rough paths theory; Stochastic Volterra equations; Fractional Brownian motion

Domaines: Probabilités [math.PR]

Aurélien Deya, Samy Tindel. Rough Volterra equations 1: the algebraic integration setting. Stochastics and Dynamics, 2009, 9, pp.437-477. ⟨10.1142/S0219493709002737⟩. ⟨hal-00320735⟩