The dynamical system response to a small variation of the right-hand side and finite-dimensional analogues of the Fokker–Planck equation

The change of a steady-state solution to the Fokker–Planck equation in response to small variations of the right-hand side (vector field) of the corresponding unperturbed system is investigated. Certain functionals of a steady-state solution and their dependence on the right-hand side of the unperturbed system are considered. This dependence is linearized, and an algorithm for computing its linear part is constructed. The applicability of the developed method to the control of dynamical systems is discussed.