Erratum on ‘‘Spectral analysis and long-time behaviour of a Fokker–Planck equation with a non-local perturbation’’

Abstract

In this article we consider a Fokker-Planck equation with a non-local, mass preserving perturbation. We show that the perturbed Fokker-Planck operator generates a C0-semigroup on an exponentially weighted L2-space. Surprisingly, the spectrum of the Fokker-Planck operator is not affected by the perturbation. In particular there still exists a unique (normalized) stationary solution of the perturbed equation. And we have convergence towards the stationary state with exponential rate −1, the same rate as for the unperturbed Fokker-Planck equation. Moreover, for any k ∈ N there exists an invariant subspace with finite codimension in which the exponential decay rate equals −k. As a byproduct of our analysis we characterize the spectrum of the Fokker-Planck operator in L2-spaces with exponential weights.