Some differential systems driven by a fBm with Hurst parameter greater than 1/4

Samy Tindel (1) , Iván Torrecilla (2)

1 IECN - Institut Élie Cartan de Nancy
2 UB - Facultat de Matemàtiques

This note is devoted to show how to push forward the algebraic integration setting in order to treat differential systems driven by a noisy input with Hölder regularity greater than 1/4. After recalling how to treat the case of ordinary stochastic differential equations, we mainly focus on the case of delay equations. A careful analysis is then performed in order to show that a fractional Brownian motion with Hurst parameter H>1/4 fulfills the assumptions of our abstract theorems.

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

Domaines: Probabilités [math.PR]

Samy Tindel, Iván Torrecilla. Some differential systems driven by a fBm with Hurst parameter greater than 1/4. 2009. ⟨hal-00352998⟩