Potential theory of infinite dimensional Levy processes

Beznea L, Cornea A, Röckner M (2011)
Journal of Functional Analysis 261(10): 2845-2876.

Zeitschriftenaufsatz | Veröffentlicht| Englisch
 
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Autor/in
Beznea, Lucian; Cornea, Aurel; Röckner, MichaelUniBi
Abstract / Bemerkung
We study the potential theory of a large class of infinite dimensional Levy processes, including Brownian motion on abstract Wiener spaces. The key result is the construction of compact Lyapunov functions, i.e., excessive functions with compact level sets. Then many techniques from classical potential theory carry over to this infinite dimensional setting. Thus a number of potential theoretic properties and principles can be proved, answering long standing open problems even for the Brownian motion on abstract Wiener space, as, e.g., formulated by R. Carmona in 1980. In particular, we prove the analog of the known result, that the Cameron Martin space is polar, in the Levy case and apply the technique of controlled convergence to solve the Dirichlet problem with general (not necessarily continuous) boundary data. (C) 2011 Elsevier Inc. All rights reserved.
Stichworte
Polar set; Capacity; process on Hilbert space; Levy; Abstract Wiener space; Infinite dimensional Brownian motion; Dirichlet problem; Lyapunov function; Controlled convergence
Erscheinungsjahr
2011
Zeitschriftentitel
Journal of Functional Analysis
Band
261
Ausgabe
10
Seite(n)
2845-2876
ISSN
0022-1236
Page URI
https://pub.uni-bielefeld.de/record/2394377

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Beznea L, Cornea A, Röckner M. Potential theory of infinite dimensional Levy processes. Journal of Functional Analysis. 2011;261(10):2845-2876.
Beznea, L., Cornea, A., & Röckner, M. (2011). Potential theory of infinite dimensional Levy processes. Journal of Functional Analysis, 261(10), 2845-2876. doi:10.1016/j.jfa.2011.07.016
Beznea, L., Cornea, A., and Röckner, M. (2011). Potential theory of infinite dimensional Levy processes. Journal of Functional Analysis 261, 2845-2876.
Beznea, L., Cornea, A., & Röckner, M., 2011. Potential theory of infinite dimensional Levy processes. Journal of Functional Analysis, 261(10), p 2845-2876.
L. Beznea, A. Cornea, and M. Röckner, “Potential theory of infinite dimensional Levy processes”, Journal of Functional Analysis, vol. 261, 2011, pp. 2845-2876.
Beznea, L., Cornea, A., Röckner, M.: Potential theory of infinite dimensional Levy processes. Journal of Functional Analysis. 261, 2845-2876 (2011).
Beznea, Lucian, Cornea, Aurel, and Röckner, Michael. “Potential theory of infinite dimensional Levy processes”. Journal of Functional Analysis 261.10 (2011): 2845-2876.