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Differential properties of semigroups and estimates of distances between stationary distributions of diffusions
- Authors: Bogachev V.I.1,2,3, Miftakhov A.F.1, Shaposhnikov S.V.1,2,3
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Affiliations:
- Lomonosov Moscow State University
- National Research University Higher School of Economics
- St. Tikhons Orthodox University
- Issue: Vol 485, No 4 (2019)
- Pages: 399-404
- Section: Mathematics
- URL: https://journals.eco-vector.com/0869-5652/article/view/13539
- DOI: https://doi.org/10.31857/S0869-56524854399-404
- ID: 13539
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Abstract
We obtain new bounds on the total variation distance and the Kantorovich distance between stationary distributions of diffusion processes in terms of certain distances between diffusion and drift coefficients.
About the authors
V. I. Bogachev
Lomonosov Moscow State University; National Research University Higher School of Economics; St. Tikhons Orthodox University
Author for correspondence.
Email: vibogach@mail.ru
Russian Federation, 1, Leninskie gory, Moscow, 119991; 20, Myasnitskaya street, Moscow, 101000; 23 5a, Novokuznetskaya street, Moscow, 115184
A. F. Miftakhov
Lomonosov Moscow State University
Email: vibogach@mail.ru
Russian Federation, 1, Leninskie gory, Moscow, 119991
S. V. Shaposhnikov
Lomonosov Moscow State University; National Research University Higher School of Economics; St. Tikhons Orthodox University
Email: vibogach@mail.ru
Russian Federation, 1, Leninskie gory, Moscow, 119991; 20, Myasnitskaya street, Moscow, 101000; 23 5a, Novokuznetskaya street, Moscow, 115184
References
- Bogachev V. I., Röckner M., Shaposhnikov S. V. // J. Funct. Anal. 2016. V. 271. P. 1262-1300.
- Богачев В. И., Кириллов А. И., Шапошников С. В. // Теория вероятностей и ее применение. 2017. Т. 62. № 1. С. 16-43.
- Bogachev V. I., Krylov N. V., Röckner M., Shaposhnikov S. V. Fokker-Planck-Kolmogorov Equations // Providence (R.I.): Amer. Math. Soc., 2015.
- Bogachev V. I., Kirillov A. I., Shaposhnikov S. V. // Math. Notes. 2014. V. 96. № 6. P. 855-863.
- Bogachev V. I., Röckner M., Shaposhnikov S. V. // J. Math. Sci. (N.Y.). 2018. V. 232. № 3. P. 254-282.
- Богачев В. И., Колесников А. В. // УМН. 2012. Т. 67. № 5. С. 3-110.
- Богачев В. И. // УМН. 2018. Т. 73. № 2. С. 3-74.
- Pardoux E., Veretennikov A.Yu. // Ann. Probab. 2001. V. 29. P. 1061-1085.
- Cattiaux P., Guillin A., Wang F.-Y., Wu L. // J. Funct. Anal. 2009. V. 256. P. 1821-1841.
- Cattiaux P., Guillin A. // J. Funct. Anal. 2017. V. 272. P. 2361-2391.
- Bogachev V. I., Röckner M., Shaposhnikov S. V. // Arxiv.org 18001.02446v1.
- Ji M., Shen Z., Yi Y. // J. Dyn. Different. Equat. 2018.
- Priola E., Wang F. Y. // J. Funct. Anal. 2006. V. 236. P. 244-264.
- Porretta A., Priola E. // J. Math. Pures and Appl. 2013. V. 100. P. 633-686.
- Arendt W., Metafune G., Pallara D. // J. Math. Anal. and Appl. 2008. V. 338. № 1. P. 505-517.
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