Rough Volterra equations 2: convolutional generalized integrals

Samy Tindel (1, 2) , Aurélien Deya (1)

1 IECN - Institut Élie Cartan de Nancy
2 BIGS - Biology, genetics and statistics

We define and solve Volterra equations driven by an irregular signal, by means of a variant of the rough path theory allowing to handle generalized integrals weighted by an exponential coefficient. The results are applied to the fractional Brownian motion with Hurst coefficient $H$ > 1/3.

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

Domaines: Probabilités [math.PR]

Samy Tindel, Aurélien Deya. Rough Volterra equations 2: convolutional generalized integrals. Stochastic Processes and their Applications, 2011, 121 (8), pp.1864-1899. ⟨10.1016/j.spa.2011.05.003⟩. ⟨hal-00328409⟩