Giuseppina Guatteri and Rainer Buckdahn

Title: "A Stochastic Tikhonov Theorem in Infinite Dimensions."


Abstract : The present paper studies the problem of singular perturbation in the infinite dimensional framework and gives a Hilbert space valued stochastic version of the Tikhonov theorem. We consider a non linear system of Hilbert space valued equations for a ``slow'' and a ``fast'' variable; the system is strongly coupled and driven by linear unbounded operators generating a $C_0$-semigroup and independent cylindrical Brownian motions. Under well established assumptions to guarantee the existence and uniqueness of mild solutions, we deduce the required stability of the system from a dissipativity condition on the drift of the fast variable. The work on this paper has been supported by the European Research Training Network "Evolution Equations for Deterministic and Stochastic Systems", Research Training Network HPRN-CT-2002-00281.