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Russian Mathematical Surveys, 2018, Volume 73, Issue 2, Pages 191–260
DOI: https://doi.org/10.1070/RM9812 (Mi rm9812) 		 
This article is cited in 31 scientific papers (total in 32 papers)

Ornstein–Uhlenbeck operators and semigroups

V. I. Bogachevab

a Lomonosov Moscow State University
b National Research University Higher School of Economics
English version PDF (1009 kB) Citations (32)
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DOI: https://doi.org/10.1070/RM9812
Abstract: This survey gives an account of the state of the art of the theory of Ornstein–Uhlenbeck operators and semigroups. The domains of definition and the spectra of such operators are considered, along with related Sobolev classes with respect to Gaussian measures. Considerable attention is given to various functional inequalities involving such operators and semigroups. Generalized Mehler semigroups are briefly discussed. Major recent achievements are presented and remaining open problems are indicated.
Bibliography: 214 titles.
Keywords: Ornstein–Uhlenbeck operator, Ornstein–Uhlenbeck semigroup, Gaussian measure, Chebyshev–Hermite polynomial, Mehler formula.
Funding agency Grant number
Russian Science Foundation 17-11-01058
This research was conducted at Lomonosov Moscow State University with the support of the Russian Science Foundation (grant no. 17-11-01058).
Received: 01.12.2017
Revised: 05.01.2018
Russian version:
Uspekhi Matematicheskikh Nauk, 2018, Volume 73, Issue 2(440), Pages 3–74
DOI: https://doi.org/10.4213/rm9812
Bibliographic databases:
Document Type: Article
UDC: 519.2
MSC: Primary 47D03, 47A05, 60H07; Secondary 46G12, 47B38, 60B11
Language: English
Original paper language: Russian
Citation: V. I. Bogachev, “Ornstein–Uhlenbeck operators and semigroups”, Uspekhi Mat. Nauk, 73:2(440) (2018), 3–74; Russian Math. Surveys, 73:2 (2018), 191–260
Citation in format AMSBIB
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    • This publication is cited in the following 32 articles:
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    References:119
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