Geodesic
The Fokker–Planck–Kolmogorov equations for some degenerate diffusion processes
Teoriâ slučajnyh processov, Tome 16 (2010) no. 1, pp. 57-66

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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.
Keywords: transition density to a process, degenerate parabolic equation, fundamental solution, Cauchy problem.
Mots-clés : Diffusion process, Fokker–Planck–Kolmogorov equation 
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     title = {The {Fokker{\textendash}Planck{\textendash}Kolmogorov} equations for some degenerate diffusion processes},
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S. D. Ivasishen; I. P. Medynsky. The Fokker–Planck–Kolmogorov equations for some degenerate diffusion processes. Teoriâ slučajnyh processov, Tome 16 (2010) no. 1, pp. 57-66. http://geodesic.mathdoc.fr/item/THSP_2010_16_1_a7/