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 Uspekhi Mat. Nauk, 1990, Volume 45, Issue 3(273), Pages 3–83 (Mi umn4736)

Analytic properties of infinite-dimensional distributions

V. I. Bogachev, O. G. Smolyanov

M. V. Lomonosov Moscow State University, Faculty of Mechanics and Mathematics

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English version:
Russian Mathematical Surveys, 1990, 45:3, 1–104

Bibliographic databases:

UDC: 519.2
MSC: 28C20, 60H07, 60Exx, 60J60

Citation: V. I. Bogachev, O. G. Smolyanov, “Analytic properties of infinite-dimensional distributions”, Uspekhi Mat. Nauk, 45:3(273) (1990), 3–83; Russian Math. Surveys, 45:3 (1990), 1–104

Citation in format AMSBIB
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Citing articles on Google Scholar: Russian citations, English citations
Related articles on Google Scholar: Russian articles, English articles

This publication is cited in the following articles:
1. V. I. Bogachev, “Functionals of random processes and infinite-dimensional oscillatory integrals connected with them”, Russian Acad. Sci. Izv. Math., 40:2 (1993), 235–266
2. A. I. Kirillov, “Two mathematical problems of canonical quantization. III. Stochastic vacuum mechanics”, Theoret. and Math. Phys., 91:3 (1992), 591–603
3. E. P. Krugova, “On the integrability of logarithmic derivatives of measures”, Math. Notes, 53:5 (1993), 506–512
4. A. I. Kirillov, “Prescription of measures on functional spaces by means of numerical densities and path integrals”, Math. Notes, 53:5 (1993), 555–557
5. N. A. Tolmachev, “A property of distributions of diffusion processes”, Math. Notes, 54:3 (1993), 946–950
6. M. U. Khafizov, “On the continuity space of product measure”, Math. Notes, 54:5 (1993), 1159–1164
7. N. V. Norin, “Ito^ Formula for an Extended Stochastic Integral with Nonanticipating Kernel”, Theory Probab Appl, 39:4 (1994), 573
8. O. G. Smolyanov, M. O. Smolyanova, “Transformations of Feynman integral under some nonlinear transformations of the phase space”, Theoret. and Math. Phys., 100:1 (1994), 803–810
9. A. I. Kirillov, “Infinite-dimensional analysis and quantum theory as semimartingale calculus”, Russian Math. Surveys, 49:3 (1994), 43–95
10. A. I. Kirillov, “Sine-Gordon type field in spacetime of arbitrary dimension. II: Stochastic quantization”, Theoret. and Math. Phys., 105:2 (1995), 1329–1345
11. M. O. Smolyanova, “Stochastic approximation of Banach-valued random variables with smooth distributions”, Math. Notes, 58:3 (1995), 970–982
12. E. P. Krugova, “Differentiability of convex measures”, Math. Notes, 58:6 (1995), 1294–1301
13. A. I. Kirillov, “On the reconstruction of measures from their logarithmic derivatives”, Izv. Math., 59:1 (1995), 121–139
14. V. I. Piterbarg, V. R. Fatalov, “The Laplace method for probability measures in Banach spaces”, Russian Math. Surveys, 50:6 (1995), 1151–1239
15. V. I. Bogachev, “Gaussian measures on linear spaces”, Journal of Mathematical Sciences (New York), 79:2 (1996), 933
16. V. I. Bogachev, “Differentiable measures and the Malliavin calculus”, Journal of Mathematical Sciences (New York), 87:4 (1997), 3577
17. E. P. Krugova, “On translates of convex measures”, Sb. Math., 188:2 (1997), 227–236
18. V. I. Bogachev, “Measures on topological spaces”, Journal of Mathematical Sciences (New York), 91:4 (1998), 3033
19. A. I. Kirillov, “Generalized differentiable product measures”, Math. Notes, 63:1 (1998), 33–49
20. Hongwei Long, “Kato's inequality and essential self-adjointness of Dirichlet operators on certain Banach spaces”, Stochastic Analysis and Applications, 16:6 (1998), 1019
21. V. Bogachev, E. Mayer-Wolf, “Dynamical systems generated by sobolev class vector fields in finite and infinite dimensions”, Journal of Mathematical Sciences (New York), 94:3 (1999), 1394
22. Vladimir Bogachev, Eduardo Mayer-Wolf, “Absolutely Continuous Flows Generated by Sobolev Class Vector Fields in Finite and Infinite Dimensions”, Journal of Functional Analysis, 167:1 (1999), 1
23. O. V. PUGACHEV, “TIGHTNESS OF SOBOLEV CAPACITIES IN INFINITE DIMENSIONAL SPACES”, Infin. Dimens. Anal. Quantum. Probab. Relat. Top, 02:03 (1999), 427
24. Hongwei Long, “Necessary and sufficient conditions for the symmetrizability of dierential operators over innite dimensional state spaces”, form, 12:2 (2000), 167
25. A. Yu. Khrennikov, H. Petersson, “A Paley–Wiener theorem for generalized entire functions on infinite-dimensional spaces”, Izv. Math., 65:2 (2001), 403–424
26. Marco Fuhrman, “Logarithmic derivatives of invariant measure for stochastic differential equations in hilbert spaces”, Stochastics and Stochastic Reports, 71:3-4 (2001), 269
27. S. V. Lyudkovskii, “Quasi-invariant and pseudo-differentiable measures with values in non-Archimedean fields on a non-Archimedean Banach space”, J. Math. Sci., 128:6 (2005), 3428–3460
28. STEFANO BONACCORSI, MARCO FUHRMAN, “INTEGRATION BY PARTS AND SMOOTHNESS OF THE LAW FOR A CLASS OF STOCHASTIC EVOLUTION EQUATIONS”, Infin. Dimens. Anal. Quantum. Probab. Relat. Top, 07:01 (2004), 89
29. V. I. Bogachev, B. Goldys, “Second derivatives of convex functions in the sense of A. D. Aleksandrov on infinite-dimensional spaces with measure”, Math. Notes, 79:4 (2006), 454–467
30. ABDELHADI ES-SARHIR, “SOBOLEV REGULARITY OF INVARIANT MEASURES FOR GENERALIZED ORNSTEIN–UHLENBECK OPERATORS”, Infin. Dimens. Anal. Quantum. Probab. Relat. Top, 09:04 (2006), 595
31. Aida Sh., Sasaki K., “Wong-Zakai Approximation of Solutions to Reflecting Stochastic Differential Equations on Domains in Euclidean Spaces”, Stoch. Process. Their Appl., 123:10 (2013), 3800–3827
32. V. I. Bogachev, I. I. Malofeev, “On the distributions of smooth functions on infinite-dimensional spaces with measures”, Dokl. Math, 89:1 (2014), 5
33. Kozlov V.V., Smolyanov O.G., “Invariant and Quasi-Invariant Measures on Infinite-Dimensional Spaces”, 92, no. 3, 2015, 743–746
34. V. I. Bogachev, “Distributions of polynomials on multidimensional and infinite-dimensional spaces with measures”, Russian Math. Surveys, 71:4 (2016), 703–749
35. Bogachev V. Smolyanov O., “Topological Vector Spaces and Their Applications”, Topological Vector Spaces and Their Applications, Springer Monographs in Mathematics, Springer, 2017, 1–456
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