Support theorem for mild solutions of SDE's in Hilbert spaces

J. Math. Sci. Univ. Tokyo
Vol. 11 (2004), No. 3, Page 245--311.

Nakayama, Toshiyuki
Support theorem for mild solutions of SDE's in Hilbert spaces
A support theorem is proven for the mild solution of the stochastic differential equation in a Hilbert space of the form: $$dX(t)=AX(t)dt+b(X(t))dt +\sigma(X(t))dB(t).$$ It is driven by a Hilbert space-valued Wiener process $B$, with the infinitesimal generator $A$ of a ($C_0$)-semigroup.