On reconstruction of Kolmogorov operators with discontinuous coefficients

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详细

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. 

作者简介

V. Bogachev

Moscow State Lomonosov University; National Research University Higher School of Economics; Saint-Tikhon's Orthodox University

编辑信件的主要联系方式.
Email: vibogach@mail.ru

Corresponding Member of the RAS

俄罗斯联邦, Moscow; Moscow; Moscow

S. Shaposhnikov

Moscow State Lomonosov University; National Research University Higher School of Economics

Email: starticle@mail.ru
俄罗斯联邦, Moscow; Moscow

参考

  1. Kolmogoroff A. // Math. Ann. 1931. B. 104. S. 415–458; русский пер.: Колмогоров А.Н. // Успехи матем. наук. 1938. Т. 5. С. 5–41.
  2. Богачев В.И., Рёкнер М., Шапошников С.В. // Теория вероятн. и ее примен. 2023. Т. 68. № 3. С. 420–455.
  3. Bogachev V.I., Krylov N.V., Röckner M., Shaposhnikov S.V. Fokker–Planck–Kolmogorov equations, Amer. Math. Soc., Providence, Rhode Island, 2015.
  4. Stroock D.W., Varadhan S.R.S. Multidimensional diffusion processes. Springer-Verlag, Berlin – New York, 1979.
  5. Rogers L.C.G., Williams D. Diffusions, Markov processes, and martingales. V. 2. Itô calculus. Cambridge University Press, Cambridge, 2000.
  6. Figalli A. // J. Funct. Anal. 2008. V. 254. N 1. P. 109–153.
  7. Trevisan D. // Electron. J. Probab. 2016. V. 21, Paper No. 22, 41 pp.
  8. Bogachev V.I., Röckner M., Shaposhnikov S.V. // J. Dynam. Differ. Equat. 2021. V. 33. N 2. P. 715–739.

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