THE FOKKER–PLANCK–KOLMOGOROV EQUATIONS FOR SOME DEGENERATE DIFFUSION PROCESSES

S. D. IVASYSHEN AND I. P. MEDYNSKY

Theory of Stochastic Processes

Vol.16 (32), no.1, 2010, pp.57-66

We clarify the connection between diffusion processes and partial differential equations of the parabolic type. The emphasis is on degenerate parabolic equations. These equations are a generalization of the classical Kolmogorov equation of diffusion with inertia which may be treated as the Fokker-Planck-Kolmogorov equations for the respectively degenerate diffusion processes. The basic results relating to the fundamental solution and the correct solvability of the Cauchy problem are presented.