OS Stochastische Analysis Detailseite Kalender

Vortragende Person/Vortragende Personen:
Prof. Dr. Davide Addona (Universita degli Studi di Milano-Bicocca, Italien)

Abstract:

We provide sufficient conditions which allow us to apply an inifinite-dimensional version of Ikeda–Watanabe theorem to the SDE

   dX(t) = AX(t)dt + GF(X(t))dt + GdW(t), (0 ≤ t ≤ T), X(0) = x (1)

which evolves in a separable Hilbert space H, when the drift term F is only β-Hölder continuous. As a byproduct, it follows that (1) admits a unique strong solution for every x in H. Here, A is the infinitesimal generator of a strongly continuous semigroup and (W) is a cylindrical Wiener process on H. The main tools to prove our result are a system of forward-backward SDEs and regularity properties of the mild solution to a suitable infinite dimensional Kolmogorov equation associated to (1). This is a joint work with Federica Masiero and Enrico Priola.