BV functions in a Gelfand triple for differentiable measure and its applications
Röckner M, Zhu R, Zhu X (2015)
Forum Mathematicum 27(3): 1657-1687.
Zeitschriftenaufsatz
| Veröffentlicht | Englisch
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Einrichtung
Abstract / Bemerkung
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 Gamma in a Banach space E. We prove the existence of a martingale solution of this problem if Gamma is a regular convex set.
Stichworte
Dirichlet forms;
BV function;
stochastic reflection problems;
Gelfand;
triples;
stochastic quantization;
integration by parts formula in infinite dimensions;
differentiable measure
Erscheinungsjahr
2015
Zeitschriftentitel
Forum Mathematicum
Band
27
Ausgabe
3
Seite(n)
1657-1687
ISSN
0933-7741
Page URI
https://pub.uni-bielefeld.de/record/2758461
Zitieren
Röckner M, Zhu R, Zhu X. BV functions in a Gelfand triple for differentiable measure and its applications. Forum Mathematicum. 2015;27(3):1657-1687.
Röckner, M., Zhu, R., & Zhu, X. (2015). BV functions in a Gelfand triple for differentiable measure and its applications. Forum Mathematicum, 27(3), 1657-1687. doi:10.1515/forum-2012-0137
Röckner, Michael, Zhu, Rongchan, and Zhu, Xiangchan. 2015. “BV functions in a Gelfand triple for differentiable measure and its applications”. Forum Mathematicum 27 (3): 1657-1687.
Röckner, M., Zhu, R., and Zhu, X. (2015). BV functions in a Gelfand triple for differentiable measure and its applications. Forum Mathematicum 27, 1657-1687.
Röckner, M., Zhu, R., & Zhu, X., 2015. BV functions in a Gelfand triple for differentiable measure and its applications. Forum Mathematicum, 27(3), p 1657-1687.
M. Röckner, R. Zhu, and X. Zhu, “BV functions in a Gelfand triple for differentiable measure and its applications”, Forum Mathematicum, vol. 27, 2015, pp. 1657-1687.
Röckner, M., Zhu, R., Zhu, X.: BV functions in a Gelfand triple for differentiable measure and its applications. Forum Mathematicum. 27, 1657-1687 (2015).
Röckner, Michael, Zhu, Rongchan, and Zhu, Xiangchan. “BV functions in a Gelfand triple for differentiable measure and its applications”. Forum Mathematicum 27.3 (2015): 1657-1687.
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