Kolmogorov problems on equations for stationary and transition probabilities of diffusion processes

V. I. Bogachev   ; M. Röckner   ; S. V. Shaposhnikov

Teoriâ veroâtnostej i ee primeneniâ, Tome 68 (2023) no. 3, pp. 420-455

Résumé

The paper gives a survey of several directions of research connected with the works of A. N. Kolmogorov on parabolic and elliptic Fokker–Planck–Kolmogorov equations for transition and stationary probabilities of diffusion processes. We present the fundamental results on existence of solutions, their uniqueness, and the properties of solution densities. Open questions in this area are mentioned.

Détail

Mots-clés : Fokker–Planck–Kolmogorov equation
Keywords: transition probability, invariant measure, Cauchy problem.

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