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Zapiski Nauchnykh Seminarov POMI, 2015, Volume 441, Pages 17–44 (Mi znsl6225)  
This article is cited in 2 scientific papers (total in 2 papers)

Equivalence of the Brownian and energy representations

S. Albeverioa, B. K. Driverb, M. Gordinac, A. M. Vershikdef

a Institut für Angewandte Mathematik Abteilung Wahrscheinlichkeitstheorie und HCM Rheinische Friedrich-Wilhelms-Universität Bonn, Endenicher Allee 60, 53115 Bonn, Germany
b Department of Mathematics, 0112, University of California, San Diego, La Jolla, CA 92093-0112, U.S.A.
c Department of Mathematics, University of Connecticut, Storrs, CT 06269, U.S.A.
d St.Petersburg Department of Steklov Institute of Mathematics, Russian Academy of Sciences, Russia
e Mathematics and Mechanics Department, St. Petersburg State University, Russia
f Institue of the Probelm of Transmission of Information, Russia
Full-text PDF (299 kB) Citations (2)
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Abstract: We consider two unitary representations of the infinite-dimensional groups of smooth paths with values in a compact Lie group. The first representation is induced by quasi-invariance of the Wiener measure, and the second representation is the energy representation. We define these representations and their basic properties, and then we prove that these representations are unitarily equivalent.
Key words and phrases: quasi-invariance, stochastic differential equations, Lie groups, representations of infinite-dimensional groups.
Funding agency Grant number
University of Bonn
National Science Foundation DMS-0739164
DMS-1007496
Russian Foundation for Basic Research 14-01-00373
Research was supported in part by CIB, EPFL and HCM, University of Bonn. This research was supported in part by NSF Grant DMS-0739164. Research was supported in part by NSF Grant DMS-1007496. Research was supported in part by RFFR Grant 14-01-00373.
Received: 19.11.2015
English version:
Journal of Mathematical Sciences (New York), 2016, Volume 219, Issue 5, Pages 612–630
DOI: https://doi.org/10.1007/s10958-016-3134-1
Bibliographic databases:
Document Type: Article
UDC: 519
Language: English
Citation: S. Albeverio, B. K. Driver, M. Gordina, A. M. Vershik, “Equivalence of the Brownian and energy representations”, Probability and statistics. Part 22, Zap. Nauchn. Sem. POMI, 441, POMI, St. Petersburg, 2015, 17–44; J. Math. Sci. (N. Y.), 219:5 (2016), 612–630
Citation in format AMSBIB
\Bibitem{AlbDriGor15}
\by S.~Albeverio, B.~K.~Driver, M.~Gordina, A.~M.~Vershik
\paper Equivalence of the Brownian and energy representations
\inbook Probability and statistics. Part~22
\serial Zap. Nauchn. Sem. POMI
\yr 2015
\vol 441
\pages 17--44
\publ POMI
\publaddr St.~Petersburg
\mathnet{http://mi.mathnet.ru/znsl6225}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=3504497}
\transl
\jour J. Math. Sci. (N. Y.)
\yr 2016
\vol 219
\issue 5
\pages 612--630
\crossref{https://doi.org/10.1007/s10958-016-3134-1}
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    • This publication is cited in the following 2 articles:
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