chapter  11
10 Pages

Large Asymptotic Behaviour of Kolmogorov Equations in Hilbert Spaces

ByGiuseppe da Prato

Let us consider a dynamical system in a separable Hilbert space H (norm |⋅|, inner product 〈 ⋅ , ⋅ 〉 ) governed by a differential stochastic equation perturbed by a cylindrical Wiener process W in H, () d X ( t )     = ( A X ( t ) + F ( X ( t ) ) ) d t + d W ( t ) ,         t     ≥     0 ,       X ( 0 )     = x ∈ H .                                                                                                                                             } where A : D(A) ⊂ H → H is a linear operator infinitesimal generator of a strongly continuous semigroup etA in H, and F : H → H is a nonlinear mapping.