Large deviation problem for some parabolic itǒ equations

Abstract The large deviation problem of Wentzell‐Freidlin type is considered for a class of semilinear parabolic equations perturbed by a small multiplicative noise. In a Hilbert space setting, it is proved that, under suitable conditions, the associated family of solution measures, depending on a small parameter, obeys the large deviation principle with respect to a certain rate function.