The stochastic reflection problem on an infinite dimensional convex set and BV functions in a Gelfand triple

Röckner M, Zhu R, Zhu X (2012)
The Annals of Probability 40(4): 1759-1794.

Zeitschriftenaufsatz | Veröffentlicht| Englisch
 
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Abstract / Bemerkung
In this paper, we introduce a definition of BV functions in a Gelfand triple which is an extension of the definition of BV functions in [Atti Accad. Naz. Lincei Cl. Sci. Fis. Mat. Natur Rend. Lincei (9) Mat. Appl. 21 (2010) 405-414] 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 in a Hilbert space H. 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 nonsymmetric 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.
Stichworte
integration by parts formula in infinite dimensions; triples; Gelfand; BV function; Dirichlet forms; stochastic reflection problems
Erscheinungsjahr
2012
Zeitschriftentitel
The Annals of Probability
Band
40
Ausgabe
4
Seite(n)
1759-1794
ISSN
0091-1798
Page URI
https://pub.uni-bielefeld.de/record/2523756

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Röckner M, Zhu R, Zhu X. The stochastic reflection problem on an infinite dimensional convex set and BV functions in a Gelfand triple. The Annals of Probability. 2012;40(4):1759-1794.
Röckner, M., Zhu, R., & Zhu, X. (2012). The stochastic reflection problem on an infinite dimensional convex set and BV functions in a Gelfand triple. The Annals of Probability, 40(4), 1759-1794. doi:10.1214/11-AOP661
Röckner, M., Zhu, R., and Zhu, X. (2012). The stochastic reflection problem on an infinite dimensional convex set and BV functions in a Gelfand triple. The Annals of Probability 40, 1759-1794.
Röckner, M., Zhu, R., & Zhu, X., 2012. The stochastic reflection problem on an infinite dimensional convex set and BV functions in a Gelfand triple. The Annals of Probability, 40(4), p 1759-1794.
M. Röckner, R. Zhu, and X. Zhu, “The stochastic reflection problem on an infinite dimensional convex set and BV functions in a Gelfand triple”, The Annals of Probability, vol. 40, 2012, pp. 1759-1794.
Röckner, M., Zhu, R., Zhu, X.: The stochastic reflection problem on an infinite dimensional convex set and BV functions in a Gelfand triple. The Annals of Probability. 40, 1759-1794 (2012).
Röckner, Michael, Zhu, Rongchan, and Zhu, Xiangchan. “The stochastic reflection problem on an infinite dimensional convex set and BV functions in a Gelfand triple”. The Annals of Probability 40.4 (2012): 1759-1794.