Stationary perturbation theory in the probability representation of quantum mechanics

In the probability representation of quantum mechanics, the eigenvalue problems in Hilbert space appear as *-genvalue equations. We show the possibility of employing the nondegenerate stationary perturbation method in the probability representation of quantum mechanics. The perturbed eigentomograms and the eigenvalues of energy are shown to be computed ab initio in terms of tomographic symbols of the operators involved.