Bogachev, Vladimir Igorevich

Statistics Math-Net.Ru
Total publications: 53
Scientific articles: 45
Presentations: 15

Number of views:
This page:12926
Abstract pages:24000
Full texts:7728
Doctor of physico-mathematical sciences (1991)
Speciality: 01.01.01 (Real analysis, complex analysis, and functional analysis)
Birth date: 14.02.1961
Keywords: Gaussian measure, differentiable measure, elliptic equation for measures, parabolic equation for measures, invariant measure of diffusion, Sobolev space.
UDC: 519.2, 517.9, 517.987, 517.972


Measure theory, probability theory, infinite dimensional analysis, stochastic analysis.

Main publications:
  1. Bogachev V.I., Gaussian measures, American Mathematical Society, Rhose Island, 1998  mathscinet  zmath
  2. Bogachev V.I., Measure theory, 1, Springer, Berlin, 2007  mathscinet  zmath
  3. Bogachev V.I., Measure theory, 2, Springer, Berlin, 2007  mathscinet
  4. Bogachev V.I., Differentiable measures and the Malliavin calculus, Regular and Chaotic Dynamics, Moscow, 2008
  5. Bogachev V.I., Smolyanov O.G., Real and functional analysis: a university course, Regular and Chaotic Dynamics, Moscow, 2009
List of publications on Google Scholar
List of publications on ZentralBlatt

Publications in Math-Net.Ru
1. Vladimir I. Bogachev, Alexander Shaposhnikov, Feng-Yu Wang, “Sobolev-–Kantorovich inequalities under $CD(0, \infty)$ condition”, Commun. Contemp. Math., 2021,  2150027–28  mathnet  scopus
2. V. I. Bogachev, “On approximation of measures by their finite-dimensional images”, Funktsional. Anal. i Prilozhen., 55:3 (2021),  75–81  mathnet
3. V. I. Bogachev, “On Sequential Properties of Spaces of Measures”, Mat. Zametki, 110:3 (2021),  459–464  mathnet; Math. Notes, 110:3 (2021), 449–453
4. V. I. Bogachev, T. I. Krasovitskii, S. V. Shaposhnikov, “On uniqueness of probability solutions of the Fokker-Planck-Kolmogorov equation”, Mat. Sb., 212:6 (2021),  3–42  mathnet; Sb. Math., 212:6 (2021), 745–781  isi
5. V. I. Bogachev, “Non-uniform Kozlov–Treschev averagings in the ergodic theorem”, Uspekhi Mat. Nauk, 75:3(453) (2020),  3–36  mathnet  mathscinet  elib; Russian Math. Surveys, 75:3 (2020), 393–425  isi  scopus
6. V. I. Bogachev, “Approximations of Nonlinear Integral Functionals of Entropy Type”, Trudy MIAN, 310 (2020),  7–18  mathnet  mathscinet  elib; Proc. Steklov Inst. Math., 310 (2020), 1–11  isi  scopus
7. Vladimir I. Bogachev, Egor D. Kosov, Svetlana N. Popova, “A new approach to Nikolskii–Besov classes”, Mosc. Math. J., 19:4 (2019),  619–654  mathnet  isi  scopus
8. V. I. Bogachev, “Ornstein–Uhlenbeck operators and semigroups”, Uspekhi Mat. Nauk, 73:2(440) (2018),  3–74  mathnet  mathscinet  elib; Russian Math. Surveys, 73:2 (2018), 191–260  isi  scopus
9. V. I. Bogachev, A. I. Kirillov, S. V. Shaposhnikov, “Distances between stationary distributions of diffusions and solvability of nonlinear Fokker–Planck–Kolmogorov equations”, Teor. Veroyatnost. i Primenen., 62:1 (2017),  16–43  mathnet  mathscinet  zmath  elib; Theory Probab. Appl., 62:1 (2018), 12–34  isi  scopus
10. V. I. Bogachev, A. N. Kalinin, S. N. Popova, “On the equality of values in the Monge and Kantorovich problems”, Zap. Nauchn. Sem. POMI, 457 (2017),  53–73  mathnet  mathscinet  zmath; J. Math. Sci. (N. Y.), 238:4 (2019), 377–389  scopus
11. V. I. Bogachev, “Distributions of polynomials on multidimensional and infinite-dimensional spaces with measures”, Uspekhi Mat. Nauk, 71:4(430) (2016),  107–154  mathnet  mathscinet  elib; Russian Math. Surveys, 71:4 (2016), 703–749  isi  scopus
12. V. I. Bogachev, A. F. Miftakhov, “On weak convergence of finite-dimensional and infinite-dimensional distributions of random processes”, Theory Stoch. Process., 21(37):1 (2016),  1–11  mathnet  mathscinet  zmath  elib  scopus
13. V. I. Bogachev, A. I. Kirillov, S. V. Shaposhnikov, “The Kantorovich and variation distances between invariant measures of diffusions and nonlinear stationary Fokker–Planck–Kolmogorov equations”, Math. Notes, 96:5 (2014), 855–863  mathnet  mathscinet  zmath
14. V. I. Bogachev, E. D. Kosov, I. Nourdin, G. Poly, “Two properties of vectors of quadratic forms of Gaussian random variables”, Teor. Veroyatnost. i Primenen., 59:2 (2014),  214–232  mathnet  mathscinet  elib; Theory Probab. Appl., 59:2 (2015), 208–221  isi  elib  scopus
15. V. I. Bogachev, A. V. Kolesnikov, “The Monge–Kantorovich problem: achievements, connections, and perspectives”, Uspekhi Mat. Nauk, 67:5(407) (2012),  3–110  mathnet  mathscinet  zmath  elib; Russian Math. Surveys, 67:5 (2012), 785–890  isi  elib  scopus
16. V. I. Bogachev, “О многочленах от гауссовских случайных величин”, Teor. Veroyatnost. i Primenen., 55:3 (2010),  611  mathnet  elib
17. V. I. Bogachev, M. Röckner, S. V. Shaposhnikov, “Lower estimates of densities of solutions of elliptic equations for measures”, Dokl. Akad. Nauk, 426:2 (2009),  156–161  mathnet  mathscinet; Dokl. Math., 79:3 (2009), 329–334  isi  scopus
18. V. I. Bogachev, N. V. Krylov, M. Röckner, “Elliptic and parabolic equations for measures”, Uspekhi Mat. Nauk, 64:6(390) (2009),  5–116  mathnet  mathscinet  elib; Russian Math. Surveys, 64:6 (2009), 973–1078  isi  elib  scopus
19. V. I. Bogachev, M. Röckner, S. V. Shaposhnikov, “Positive Densities of Transition Probabilities of Diffusion Processes”, Teor. Veroyatnost. i Primenen., 53:2 (2008),  213–239  mathnet  elib; Theory Probab. Appl., 53:2 (2009), 194–215  isi  scopus
20. V. I. Bogachev, M. Röckner, S. V. Shaposhnikov, “Estimates of densities of stationary distributions and transition probabilities of diffusion processes”, Teor. Veroyatnost. i Primenen., 52:2 (2007),  240–270  mathnet  mathscinet  zmath  elib; Theory Probab. Appl., 52:2 (2008), 209–236  isi  elib  scopus
21. V. I. Bogachev, B. Goldys, “Second derivatives of convex functions in the sense of A. D. Aleksandrov on infinite-dimensional spaces with measure”, Mat. Zametki, 79:4 (2006),  488–504  mathnet  mathscinet  zmath  elib; Math. Notes, 79:4 (2006), 454–467  isi  elib  scopus
22. V. I. Bogachev, A. V. Kolesnikov, K. V. Medvedev, “Triangular transformations of measures”, Mat. Sb., 196:3 (2005),  3–30  mathnet  mathscinet  zmath  elib; Sb. Math., 196:3 (2005), 309–335  isi  elib  scopus
23. V. I. Bogachev, M. Röckner, S. V. Shaposhnikov, “Global regularity and estimates for solutions of parabolic equations”, Teor. Veroyatnost. i Primenen., 50:4 (2005),  652–674  mathnet  mathscinet  zmath  elib; Theory Probab. Appl., 50:4 (2006), 561–581  isi
24. V. I. Bogachev, A. V. Kolesnikov, “Integrability of absolutely continuous measure transformations and applications to optimal transportation”, Teor. Veroyatnost. i Primenen., 50:3 (2005),  433–456  mathnet  mathscinet  zmath  elib; Theory Probab. Appl., 50:3 (2006), 367–385  isi  elib
25. V. I. Bogachev, A. V. Kolesnikov, “Nonlinear transformations of convex measures”, Teor. Veroyatnost. i Primenen., 50:1 (2005),  27–51  mathnet  mathscinet  zmath  elib; Theory Probab. Appl., 50:1 (2006), 34–52  isi
26. V. I. Bogachev, M. Röckner, “On $L^p$-uniqueness of symmetric diffusion operators on Riemannian manifolds”, Mat. Sb., 194:7 (2003),  15–24  mathnet  mathscinet  zmath  elib; Sb. Math., 194:7 (2003), 969–978  isi  scopus
27. V. I. Bogachev, M. Röckner, W. Stannat, “Uniqueness of solutions of elliptic equations and uniqueness of invariant measures of diffusions”, Mat. Sb., 193:7 (2002),  3–36  mathnet  mathscinet  zmath  elib; Sb. Math., 193:7 (2002), 945–976  isi  scopus
28. T. O. Banakh, V. I. Bogachev, A. V. Kolesnikov, “Topological spaces with Prokhorov and Skorokhod properties”, Dokl. Akad. Nauk, 380:6 (2001),  727–730  mathnet  mathscinet  zmath; Dokl. Math., 64:2 (2001), 244–247  isi
29. V. I. Bogachev, A. V. Kolesnikov, “Open Mappings of Probability Measures and the Skorokhod Representation Theorem”, Teor. Veroyatnost. i Primenen., 46:1 (2001),  3–27  mathnet  mathscinet  zmath; Theory Probab. Appl., 46:1 (2002), 20–38  isi
30. V. I. Bogachev, M. Röckner, “A generalization of Khasminskii's theorem on the existence of invariant measures for locally integrable drifts”, Teor. Veroyatnost. i Primenen., 45:3 (2000),  417–436  mathnet  mathscinet  zmath; Theory Probab. Appl., 45:3 (2001), 363–378  isi
31. D. E. Aleksandrova, V. I. Bogachev, A. Yu. Pilipenko, “On the convergence of induced measures in variation”, Mat. Sb., 190:9 (1999),  3–20  mathnet  mathscinet  zmath; Sb. Math., 190:9 (1999), 1229–1245  isi  scopus
32. V. I. Bogachev, “On the small balls problem for equivalent Gaussian measures”, Mat. Sb., 189:5 (1998),  47–68  mathnet  mathscinet  zmath; Sb. Math., 189:5 (1998), 683–705  isi  scopus
33. V. I. Bogachev, “Onsager–Machlup functions for Gaussian measures”, Dokl. Akad. Nauk, 344:4 (1995),  439–441  mathnet  mathscinet  zmath
34. V. I. Bogachev, “Functionals of random processes and infinite-dimensional oscillatory integrals connected with them”, Izv. RAN. Ser. Mat., 56:2 (1992),  243–278  mathnet  mathscinet  zmath; Russian Acad. Sci. Izv. Math., 40:2 (1993), 235–266  isi
35. V. I. Bogachev, “Distributions of analytic functionals of random processes”, Dokl. Akad. Nauk SSSR, 312:6 (1990),  1291–1296  mathnet  mathscinet  zmath; Dokl. Math., 41:3 (1990), 517–522
36. V. I. Bogachev, O. G. Smolyanov, “Analytic properties of infinite-dimensional distributions”, Uspekhi Mat. Nauk, 45:3(273) (1990),  3–83  mathnet  mathscinet  zmath; Russian Math. Surveys, 45:3 (1990), 1–104  isi
37. V. I. Bogachev, Yu. I. Prostov, “A polynomial diffeomorphism of a ball without invariant measures”, Funktsional. Anal. i Prilozhen., 23:4 (1989),  75–76  mathnet  mathscinet  zmath; Funct. Anal. Appl., 23:4 (1989), 317–319  isi
38. V. I. Bogachev, “Subspaces of the differentiability of smooth measures on infinite-dimensional spaces”, Dokl. Akad. Nauk SSSR, 299:1 (1988),  18–22  mathnet  mathscinet  zmath; Dokl. Math., 37:2 (1988), 304–308
39. V. I. Bogachev, S. A. Shkarin, “Differentiable and Lipschitzian mappings of Banach spaces”, Mat. Zametki, 44:5 (1988),  567–583  mathnet  mathscinet  zmath; Math. Notes, 44:5 (1988), 790–798  isi
40. V. I. Bogachev, “On Skorokhod's Differentiability of Measures”, Teor. Veroyatnost. i Primenen., 33:2 (1988),  349–354  mathnet  mathscinet  zmath; Theory Probab. Appl., 33:2 (1988), 330–334  isi
41. V. I. Bogachev, “The asymmetry indices of stable measures”, Mat. Zametki, 40:1 (1986),  127–138  mathnet  mathscinet  zmath; Math. Notes, 40:1 (1986), 569–575  isi
42. V. I. Bogachev, “Locally convex spaces with the CLT property and supports of measures”, Vestnik Moskov. Univ. Ser. 1. Mat. Mekh., 1986, 6,  16–20  mathnet  mathscinet  zmath
43. V. I. Bogachev, “Some results on differentiable measures”, Mat. Sb. (N.S.), 127(169):3(7) (1985),  336–351  mathnet  mathscinet  zmath; Math. USSR-Sb., 55:2 (1986), 335–349
44. V. I. Bogachev, “Three problems of aronszajn in measure theory”, Funktsional. Anal. i Prilozhen., 18:3 (1984),  75–76  mathnet  mathscinet  zmath; Funct. Anal. Appl., 18:3 (1984), 242–244  isi
45. V. I. Bogachev, “Full access to content Negligible sets in locally convex spaces”, Mat. Zametki, 36:1 (1984),  51–64  mathnet  mathscinet  zmath
46. V. I. Bogachev, “Negligible sets and differentiable measures in Banach spaces”, Vestnik Moskov. Univ. Ser. 1. Mat. Mekh., 1982, 3,  47–52  mathnet  mathscinet  zmath

47. V. I. Bogachev, I. V. Volovich, B. S. Kashin, V. V. Kozlov, V. P. Maslov, V. A. Sadovnichii, A. M. Stepin, V. M. Tikhomirov, A. Yu. Khrennikov, E. T. Shavgulidze, “Oleg Georgievich Smolyanov (on his 80th birthday)”, Uspekhi Mat. Nauk, 74:4(448) (2019),  191–193  mathnet  mathscinet  elib; Russian Math. Surveys, 74:4 (2019), 771–773  isi
48. Yu. A. Alkhutov, I. V. Astashova, V. I. Bogachev, V. N. Denisov, V. V. Kozlov, S. E. Pastukhova, A. L. Piatnitski, V. A. Sadovnichii, A. M. Stepin, A. S. Shamaev, A. A. Shkalikov, “Vasilii Vasil'evich Zhikov (obituary)”, Uspekhi Mat. Nauk, 73:3(441) (2018),  169–176  mathnet  mathscinet  elib; Russian Math. Surveys, 73:3 (2018), 533–542  isi
49. I. V. Arzhantsev, V. I. Bogachev, A. I. Garber, A. A. Zaslavskii, V. Yu. Protassov, A. B. Skopenkov, “Студенческие олимпиады мехмата МГУ 2010–2011 гг.”, Mat. Pros., Ser. 3, 16 (2012),  214–227  mathnet
50. I. V. Arzhantsev, V. I. Bogachev, A. A. Zaslavskii, V. Yu. Protassov, A. M. Raigorodskii, A. B. Skopenkov, “Студенческие олимпиады мехмата МГУ”, Mat. Pros., Ser. 3, 14 (2010),  225–234  mathnet
51. V. I. Bogachev, V. S. Vladimirov, I. V. Volovich, B. S. Kashin, A. I. Kirillov, V. V. Kozlov, V. P. Maslov, V. A. Sadovnichii, A. M. Stepin, V. M. Tikhomirov, A. V. Uglanov, A. Yu. Khrennikov, A. M. Chebotarev, E. T. Shavgulidze, “Oleg Georgievich Smolyanov (on his 70th birthday)”, Uspekhi Mat. Nauk, 64:1(385) (2009),  175–177  mathnet  mathscinet  zmath  elib; Russian Math. Surveys, 64:1 (2009), 183–185  isi
52. V. I. Bogachev, A. M. Raigorodskii, A. B. Skopenkov, N. A. Tolmachev, “Студенческие олимпиады и межкафедральный семинар на мехмате Московского государственного университета”, Mat. Pros., Ser. 3, 12 (2008),  205–222  mathnet
53. V. I. Bogachev, M. Röckner, “Letter to the editors”, Teor. Veroyatnost. i Primenen., 46:3 (2001),  600  mathnet  mathscinet
54. V. S. Vladimirov, V. A. Sadovnichii, P. L. Ul'yanov, R. A. Minlos, V. I. Bogachev, A. M. Stepin, A. V. Uglanov, E. T. Shavgulidze, “Oleg Georgievitch Smolyanov (to 60th anniversary)”, Vestnik Moskov. Univ. Ser. 1. Mat. Mekh., 1998, 5,  69–70  mathnet  mathscinet

Presentations in Math-Net.Ru
1. Chebyshev-Hermite polynomials and distributions of polynomials in Gaussian random variables
Vladimir Bogachev
International Conference "Theory of Probability and Its Applications: P. L. Chebyshev – 200" (The 6th International Conference on Stochastic Methods)
May 19, 2021 16:00   
2. Elliptic Equations for Measures
V. I. Bogachev
Complex analysis and mathematical physics
March 9, 2021 16:00
3. Uniqueness problems for the Fokker-Planck-Kolmogorov equations
V. I. Bogachev
Principle Seminar of the Department of Probability Theory, Moscow State University
March 3, 2021 16:45
4. Задачи Монжа и Канторовича
V. I. Bogachev
Differential equations, analysis and control: theory and applications
March 16, 2020 18:30
5. The ergodic theorem in the Kozlov–Treschev form
V. I. Bogachev
International Conference "Classical Mechanics, Dynamical Systems and Mathematical Physics" on the occasion of V. V. Kozlov 70th birthday
January 24, 2020 10:45   
6. Fokker–Planck–Kolmogorov equations: the main achievements and open problems
V. I. Bogachev
Steklov Mathematical Institute Seminar
June 20, 2019 16:00   
7. Стационарные уравнения Колмогорова: недавние достижения и открытые проблемы
V. I. Bogachev
Seminar on Theory of Functions of Real Variables
April 19, 2019 18:30
8. Совместное заседание Московского математического общества и кафедры теории функций и функционального анализа механико-математического МГУ, посвященное 100-летию Георгия Евгеньевича Шилова
V. I. Bogachev, O. G. Smolyanov, V. M. Tikhomirov
Meetings of the Moscow Mathematical Society
November 7, 2017
9. Описание классов Никольского-Бесова через интегрирование по частям
V. I. Bogachev
Seminar on Theory of Functions of Several Real Variables and Its Applications to Problems of Mathematical Physics
February 22, 2017 16:00   
10. Monge and Kantorovich problems, spaces of measures, and Gromov triples
V. I. Bogachev
Globus Seminar
May 19, 2016 15:40   
11. Один подкласс класса Никольского-Бесова, связанный с распределениями многочленов от многих переменных
V. I. Bogachev, E. D. Kosov
Seminar on Theory of Functions of Real Variables
April 1, 2016 18:30
12. Prokhorov's Theorem and the Topology of Spaces of Probability Measures
V. I. Bogachev
International Scientific Conference "Probability Theory and its Applications" On Occasion of 85th Birthday of Yu. V. Prokhorov
February 13, 2015 17:15   
13. Kantorovich distances and the geometry of spaces of probability measures
V. I. Bogachev
Principle Seminar of the Department of Probability Theory, Moscow State University
October 10, 2012 16:45
14. Эргодическая теорема в форме Козлова–Трещева и связанные с ней результаты и открытые проблемы
V. I. Bogachev
Seminar of the Department of Mathematical Physics, Steklov Mathematical Institute of RAS
March 27, 2008 11:00
15. О недавних результатах, связанных с нелинейными преобразованиями мер и задачей Монжа–Канторовича
V. I. Bogachev
Principle Seminar of the Department of Probability Theory, Moscow State University
February 22, 2006

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