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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 32 scientific papers (total in 33 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 (33) Russian version article
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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
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”, Russian Math. Surveys, 73:2 (2018), 191–260
Citation in format AMSBIB
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\paper Ornstein--Uhlenbeck operators and semigroups
\jour Russian Math. Surveys
\yr 2018
\vol 73
\issue 2
\pages 191--260
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    • This publication is cited in the following 33 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    Abstract page:1300
    Russian version PDF:421
    English version PDF:142
    References:126
    First page:128
     
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