Kolmogorov Problems on Equations for Stationary and Transition Probabilities of Diffusion Processes
Bogachev VI, Röckner M, Shaposhnikov SV (2023)
Theory of Probability and its Applications 68(3): 342-369.
Zeitschriftenaufsatz
| Veröffentlicht | Englisch
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Autor*in
Bogachev, V. I.;
Röckner, MichaelUniBi;
Shaposhnikov, S. V.
Einrichtung
Abstract / Bemerkung
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.
Stichworte
Fokker-Planck-Kolmogorov equation;
transition probability;
invariant;
measure;
Cauchy problem
Erscheinungsjahr
2023
Zeitschriftentitel
Theory of Probability and its Applications
Band
68
Ausgabe
3
Seite(n)
342-369
ISSN
0040-585X
eISSN
1095-7219
Page URI
https://pub.uni-bielefeld.de/record/2987158
Zitieren
Bogachev VI, Röckner M, Shaposhnikov SV. Kolmogorov Problems on Equations for Stationary and Transition Probabilities of Diffusion Processes. Theory of Probability and its Applications. 2023;68(3):342-369.
Bogachev, V. I., Röckner, M., & Shaposhnikov, S. V. (2023). Kolmogorov Problems on Equations for Stationary and Transition Probabilities of Diffusion Processes. Theory of Probability and its Applications, 68(3), 342-369. https://doi.org/10.1137/S0040585X97T991507
Bogachev, V. I., Röckner, Michael, and Shaposhnikov, S. V. 2023. “Kolmogorov Problems on Equations for Stationary and Transition Probabilities of Diffusion Processes”. Theory of Probability and its Applications 68 (3): 342-369.
Bogachev, V. I., Röckner, M., and Shaposhnikov, S. V. (2023). Kolmogorov Problems on Equations for Stationary and Transition Probabilities of Diffusion Processes. Theory of Probability and its Applications 68, 342-369.
Bogachev, V.I., Röckner, M., & Shaposhnikov, S.V., 2023. Kolmogorov Problems on Equations for Stationary and Transition Probabilities of Diffusion Processes. Theory of Probability and its Applications, 68(3), p 342-369.
V.I. Bogachev, M. Röckner, and S.V. Shaposhnikov, “Kolmogorov Problems on Equations for Stationary and Transition Probabilities of Diffusion Processes”, Theory of Probability and its Applications, vol. 68, 2023, pp. 342-369.
Bogachev, V.I., Röckner, M., Shaposhnikov, S.V.: Kolmogorov Problems on Equations for Stationary and Transition Probabilities of Diffusion Processes. Theory of Probability and its Applications. 68, 342-369 (2023).
Bogachev, V. I., Röckner, Michael, and Shaposhnikov, S. V. “Kolmogorov Problems on Equations for Stationary and Transition Probabilities of Diffusion Processes”. Theory of Probability and its Applications 68.3 (2023): 342-369.
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