Vladimir I. Bogachev
Vladimir I. Bogachev | |
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| Born | 1961 |
| Nationality | Russian |
| Citizenship | Russia |
| Alma mater | Moscow State University |
| Occupation | Mathematician |
Vladimir I. Bogachev (born in 1961) is a Russian mathematician, Full Professor of the Department of Mechanics and Mathematics of the Lomonosov Moscow State University. He is one of the leading world's experts in measure theory, probability theory, infinite-dimensional analysis and partial differential equations [1]. His research was distinguished by several awards including the medal and the prize of the Academy of Sciences of the USSR (1990); Award of the Japan Society of Promotion of Science (2000); the Doob Lecture of the Bernoulli Society (2017); and the Kolmogorov Prize of the Russian Academy of Sciences (2018).
Biography
Graduated with honours from Moscow State University (1983). In 1986, he got his PhD (Candidate of Sciences in Russia) under the supervision of Prof. O. G. Smolyanov.
Awards
- The medal and the prize of the Academy of Sciences of the USSR (1990)
- Award of the Japan Society of Promotionof Science (2000)
- The Doob Lecture of the Bernoulli Society (2017) [2]
- The Kolmogorov Prize of the Russian Academy of Sciences (2018)
Scientific Contributions
In 1984, V. Bogachev resolved three Aronshain's problems on infinite-dimensional probability distributions and answered a famous question of I. M. Gelfand posed about 25 years before that. In 1992, Vladimir Bogachev proved T. Pitcher’s conjecture (stated in 1961) on the differentiability of the distributions of diffusion processes. In 1995, he proved (with M. Roeckner) the famous Shigekawa conjecture on the absolute continuity of invariant measures of diffusion processe. In 1999, in a joint work with S. Albeverio and M. Roeckner, Professor Bogachev resolved the well-known problem of S. R. S. Varadan on the uniqueness of stationary distributions, which has been remained open during about 20 years.
A remarkable achievement of Vladimir Bogachev is the recently obtained (2021) answer to the question of A. N. Kolmogorov (posed in 1931) on the uniqueness of the solution to the Cauchy problem: it isshown that the Cauchy problem with a unit diffusion coefficient and locally bounded drift hasa unique probabilistic solution on <math>\R^1</math>, and in <math>\R^{>1}</math> this is not true even for smooth drift.[3] [4]
Main Publications
Papers:
- Bogachev V.I., Röckner M. Regularity of invariant measures on finite and infinite dimen-sional spaces and applications. J. Funct. Anal., V. 133, N 1, P. 168–223 (1995)
- Albeverio S., Bogachev V.I., Röckner M. On uniqueness of invariant measures for finite and infinite dimensional diffusions. Comm. Pure Appl. Math., V. 52, P. 325–362 (1999)
- Bogachev V.I., Krasovitskii T.I., Shaposhnikov S.V. On uniqueness of probability solutions of the Fokker–Planck–Kolmogorov equation, Sb. Math., V. 212, N 6, P. 745–781 (2021)
References
External links
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