The 1-d stochastic wave equation driven by a fractional Brownian motion

Lluis Quer-Sardanyons (1) , Samy Tindel (2)

1 OMEGA - Probabilistic numerical methods
2 IECN - Institut Élie Cartan de Nancy

In this paper, we develop a Young integration theory in dimension 2 which will allow us to solve a non-linear one dimensional wave equation driven by an arbitrary signal whose rectangular increments satisfy some Hölder regularity conditions, for some Hölder exponent greater than 1/2. This result will be applied to the infinite dimensional fractional Brownian motion.

Mots clés: Wave equation; Fractional Brownian motion; Young integration

Domaines: Probabilités [math.PR]

Lluis Quer-Sardanyons, Samy Tindel. The 1-d stochastic wave equation driven by a fractional Brownian motion. Stochastic Processes and their Applications, 2007, 117, pp.1448-1472. ⟨10.1016/j.spa.2007.01.009⟩. ⟨hal-00022685⟩