Email this article 
On reconstruction of Kolmogorov operators with discontinuous coefficients
- Authors: Bogachev V.I.1,2,3, Shaposhnikov S.V.1,2
-
Affiliations:
- Moscow State Lomonosov University
- National Research University Higher School of Economics
- Saint-Tikhon's Orthodox University
- Issue: Vol 516, No 1 (2024)
- Pages: 5-8
- Section: MATHEMATICS
- URL: https://rjeid.com/2686-9543/article/view/647940
- DOI: https://doi.org/10.31857/S2686954324020018
- EDN: https://elibrary.ru/XJFWEY
- ID: 647940
Cite item
Open Access
Access granted
Subscription Access
Abstract
We obtain broad sufficient conditions for reconstructing the coefficients of a Kolmogorov operator by means of a solution to the Cauchy problem for the corresponding Fokker–Planck–Kolmogorov equation.
About the authors
V. I. Bogachev
Moscow State Lomonosov University; National Research University Higher School of Economics; Saint-Tikhon's Orthodox University
Author for correspondence.
Email: vibogach@mail.ru
Corresponding Member of the RAS
Russian Federation, Moscow; Moscow; MoscowS. V. Shaposhnikov
Moscow State Lomonosov University; National Research University Higher School of Economics
Email: starticle@mail.ru
Russian Federation, Moscow; Moscow
References
- Kolmogoroff A. // Math. Ann. 1931. B. 104. S. 415–458; русский пер.: Колмогоров А.Н. // Успехи матем. наук. 1938. Т. 5. С. 5–41.
- Богачев В.И., Рёкнер М., Шапошников С.В. // Теория вероятн. и ее примен. 2023. Т. 68. № 3. С. 420–455.
- Bogachev V.I., Krylov N.V., Röckner M., Shaposhnikov S.V. Fokker–Planck–Kolmogorov equations, Amer. Math. Soc., Providence, Rhode Island, 2015.
- Stroock D.W., Varadhan S.R.S. Multidimensional diffusion processes. Springer-Verlag, Berlin – New York, 1979.
- Rogers L.C.G., Williams D. Diffusions, Markov processes, and martingales. V. 2. Itô calculus. Cambridge University Press, Cambridge, 2000.
- Figalli A. // J. Funct. Anal. 2008. V. 254. N 1. P. 109–153.
- Trevisan D. // Electron. J. Probab. 2016. V. 21, Paper No. 22, 41 pp.
- Bogachev V.I., Röckner M., Shaposhnikov S.V. // J. Dynam. Differ. Equat. 2021. V. 33. N 2. P. 715–739.
Supplementary files
