Stochastic Volterra equations driven by Gaussian noise

Bonaccorsi Stefano, Università degli Studi di Trento
Bianchi Luigi Amedeo, Università di Trento

We study stochastic Volterra equations in Hilbert spaces driven by cylindrical Gaussian noise. We derive a mild formulation for the stochastic Volterra equation, prove the equivalence of mild and strong solutions, the existence and uniqueness of mild solutions, and study space-time regularity. Furthermore, we establish the stability of mild solutions in $L^q(\mathbb R_+)$, prove the existence of limit distributions in the Wasserstein $p$-distance with $p \in [1,\infty)$, and characterise when these limit distributions are independent of the initial state of the process despite the presence of memory. While our techniques allow for a general class of Volterra kernels, they are particularly suited for completely monotone kernels and fractional Riemann-Liouville kernels in the full range $\alpha \in (0,2)$. This presentation is based on a joint work with Luigi Amedeo Bianchi (Trento) and Martin Friesen (Dublin City University).

Area: CS7 - Advances in SPDEs (Giuseppina Guatteri and Federica Masiero)

Keywords: Stochastic Volterra equations, completely monotone kernels, limit distributions

Please Login in order to download this file