Abstract
We obtain upper bounds for the total variation and entropy distances between probability solutions to two Fokker–Planck–Kolmogorov equations with different diffusion matrices and drifts
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
V. I. Bogachev, N. V. Krylov, and M. Röckner, Russ. Math. Surv. 64 (6), 973–1078 (2009).
V. I. Bogachev and A. V. Kolesnikov, Russ. Math. Surv. 67 (5), 785–890 (2012).
V. I. Bogachev, Measure Theory (Springer, Berlin, 2007), Vol. 1.
F. Bolley and C. Villani, Ann. Fac. Sci. Toulouse Math. 14 (3), 331–352 (2005).
V. I. Bogachev, M. Röckner, and S. V. Shaposhnikov, Theory Probab. Appl. 50 (4), 561–581 (2006).
Yu. M. Kabanov, R. Sh. Liptser, and A. N. Shiryaev, Probab. Theory Relat. Fields 71 (1), 19–35 (1986).
F. Liese, Statistics 17 (1), 63–78 (1986).
J. A. Carrillo, R. J. McCann, and C. Villani, Rev. Math. Iberoamer 19, 971–1018 (2003).
L. Natile, M. A. Peletier, and G. Savaré, J. Math. Pures Appl. 95 (1), 18–35 (2011).
V. I. Bogachev, M. Röckner, and S. V. Shaposhnikov, J. Math. Sci. (New York) 179 (1), 7–47 (2011).
R. L. Dobrushin, Funct. Anal. Appl. 13 (2), 115–123 (1979).
O. A. Manita and S. V. Shaposhnikov, St. Petersburg Math. 25 (1), 43–62 (2014).
E. Pardoux and A. Yu. Veretennikov, Ann. Probab. 31 (3), 1166–1192 (2003).
A. Yu. Veretennikov, J. Math. Sci. (New York) 179 (1), 48–79 (2011).
V. I. Bogachev, A. Yu. Veretennikov, and S. V. Shaposhnikov, Dokl. Math. 91 (1), 76–79 (2015).
Author information
Authors and Affiliations
Corresponding author
Additional information
Published in Russian in Doklady Akademii Nauk, 2016, Vol. 467, No. 1, pp. 13–17.
The article was translated by the authors.
Rights and permissions
About this article
Cite this article
Bogachev, V.I., Röckner, M. & Shaposhnikov, S.V. Estimates of distances between transition probabilities of diffusions. Dokl. Math. 93, 135–139 (2016). https://doi.org/10.1134/S1064562416020034
Received:
Published:
Issue Date:
DOI: https://doi.org/10.1134/S1064562416020034