BV functions in a Gelfand triple and the stochastic reflection problem on a convex set of a Hilbert space

Röckner M, Zhu R, Zhu X (2010)
Comptes Rendus Mathematique 348(21-22): 1175-1178.

Zeitschriftenaufsatz | Veröffentlicht| Englisch
 
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Abstract / Bemerkung
In this Note we Introduce BV functions in a Gelfand triple which is an extension of BV functions in Ambrosio et al preprint [1] by using Dirichlet form theory By this definition we can consider the stochastic reflection problem associated with a self adjoint operator A and a cylindrical Wiener process on a convex set Gamma We prove the existence and uniqueness of a strong solution of this problem when Gamma is a regular convex set The result is also extended to the non symmetric case Finally we extend our results to the case when Gamma = K-alpha where K-alpha = {f is an element of L-2(0 1) vertical bar f >= -alpha} alpha >= 0 (C) 2010 Academie des sciences Published by Elsevier Masson SAS All rights reserved
Erscheinungsjahr
2010
Zeitschriftentitel
Comptes Rendus Mathematique
Band
348
Ausgabe
21-22
Seite(n)
1175-1178
ISSN
1631-073X
Page URI
https://pub.uni-bielefeld.de/record/1968087

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Röckner M, Zhu R, Zhu X. BV functions in a Gelfand triple and the stochastic reflection problem on a convex set of a Hilbert space. Comptes Rendus Mathematique. 2010;348(21-22):1175-1178.
Röckner, M., Zhu, R., & Zhu, X. (2010). BV functions in a Gelfand triple and the stochastic reflection problem on a convex set of a Hilbert space. Comptes Rendus Mathematique, 348(21-22), 1175-1178. doi:10.1016/j.crma.2010.10.018
Röckner, M., Zhu, R., and Zhu, X. (2010). BV functions in a Gelfand triple and the stochastic reflection problem on a convex set of a Hilbert space. Comptes Rendus Mathematique 348, 1175-1178.
Röckner, M., Zhu, R., & Zhu, X., 2010. BV functions in a Gelfand triple and the stochastic reflection problem on a convex set of a Hilbert space. Comptes Rendus Mathematique, 348(21-22), p 1175-1178.
M. Röckner, R. Zhu, and X. Zhu, “BV functions in a Gelfand triple and the stochastic reflection problem on a convex set of a Hilbert space”, Comptes Rendus Mathematique, vol. 348, 2010, pp. 1175-1178.
Röckner, M., Zhu, R., Zhu, X.: BV functions in a Gelfand triple and the stochastic reflection problem on a convex set of a Hilbert space. Comptes Rendus Mathematique. 348, 1175-1178 (2010).
Röckner, Michael, Zhu, Rongchan, and Zhu, Xiangchan. “BV functions in a Gelfand triple and the stochastic reflection problem on a convex set of a Hilbert space”. Comptes Rendus Mathematique 348.21-22 (2010): 1175-1178.