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Forum Mathematicum

Managing Editor: Bruinier, Jan Hendrik

Ed. by Blomer, Valentin / Cohen, Frederick R. / Droste, Manfred / Duzaar, Frank / Echterhoff, Siegfried / Frahm, Jan / Gordina, Maria / Shahidi, Freydoon / Sogge, Christopher D. / Takayama, Shigeharu / Wienhard, Anna


IMPACT FACTOR 2018: 0.867

CiteScore 2018: 0.71

SCImago Journal Rank (SJR) 2018: 0.898
Source Normalized Impact per Paper (SNIP) 2018: 0.964

Mathematical Citation Quotient (MCQ) 2018: 0.71

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1435-5337
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Volume 27, Issue 3

Issues

BV functions in a Gelfand triple for differentiable measure and its applications

Michael Röckner / Rongchan Zhu
  • Department of Mathematics, Beijing Institute of Technology, Beijing 100081, P. R. China; and Department of Mathematics, University of Bielefeld, 33615 Bielefeld, Germany
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/ Xiangchan Zhu
  • School of Sciences, Beijing Jiaotong University, Beijing 100044, P. R. China; and Department of Mathematics, University of Bielefeld, 33615 Bielefeld, Germany
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Published Online: 2013-05-15 | DOI: https://doi.org/10.1515/forum-2012-0137

Abstract

In this paper, we introduce a definition of BV functions for (non-Gaussian) differentiable measure in a Gelfand triple which is an extension of the definition of BV functions in [Ann. Probab. 40 (2012), 1759–1794], using Dirichlet form theory. By this definition, we can analyze the reflected stochastic quantization problem associated with a self-adjoint operator A and a cylindrical Wiener process on a convex set Γ in a Banach space E. We prove the existence of a martingale solution of this problem if Γ is a regular convex set.

Keywords: Dirichlet forms; stochastic reflection problems; BV function; Gelfand triples; integration by parts formula in infinite dimensions; differentiable measure; stochastic quantization

MSC: 60Gxx; 31C25; 60G60; 26A45

About the article

Received: 2012-09-12

Revised: 2013-03-13

Published Online: 2013-05-15

Published in Print: 2015-05-01


Funding Source: DFG

Award identifier / Grant number: IRTG 1132

Funding Source: DFG

Award identifier / Grant number: CRC 701


Citation Information: Forum Mathematicum, Volume 27, Issue 3, Pages 1657–1687, ISSN (Online) 1435-5337, ISSN (Print) 0933-7741, DOI: https://doi.org/10.1515/forum-2012-0137.

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Citing Articles

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[1]
Giuseppe Da Prato, Alessandra Lunardi, and Luciano Tubaro
Milan Journal of Mathematics, 2019, Volume 87, Number 1, Page 93
[2]
Michael Röckner, Rongchan Zhu, and Xiangchan Zhu
Journal of Functional Analysis, 2017, Volume 272, Number 10, Page 4263
[3]
Vladimir I. Bogachev and Ilya I. Malofeev
Potential Analysis, 2016, Volume 44, Number 4, Page 767

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