Existence of global fundamental solution to a class of Fokker–Planck equations

In this paper, we investigate global solvability of the Fokker–Planck equations of a special type. Such equations arise in models of the primary visual cortex of the human brain and describe a process of anisotropic blurring of the image of the visual field on the retina of the eye. By modifying the Folland lifting technique for linear hypoelliptic differential operators satisfying the Hormander condition, we propose a method to saturate the system of vector fields in the equation to a basis of the tangent space at every point. We present the conditions that guarantee existence of a global fundamental solution to the considered equations.