Singular HJB equations with applications to KPZ on the real line
Zhang X, Zhu R, Zhu X (2022)
Probability Theory and Related Fields 183(3-4): 789-869.
Zeitschriftenaufsatz
| Veröffentlicht | Englisch
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Abstract / Bemerkung
This paper is devoted to studying Hamilton-Jacobi-Bellman equations with distribution-valued coefficients, which are not well-defined in the classical sense and are understood by using the paracontrolled distribution method introduced in (Gubinelli et al. in Forum Math Pi 3(6):1, 2015). By a new characterization of weighted Hölder spaces and Zvonkin’s transformation we prove some new a priori estimates, and therefore establish the global well-posedness for singular HJB equations. As applications, we obtain global well-posedness in polynomial weighted Hölder spaces for KPZ type
equations on the real line, as well as modified KPZ equations for which the Cole–Hopf transformation is not applicable.
Stichworte
Singular SPDEs · HJB equations · KPZ equations · Paracontrolled distributions · Global well-posedness · Zvonkin’s transformation
Erscheinungsjahr
2022
Zeitschriftentitel
Probability Theory and Related Fields
Band
183
Ausgabe
3-4
Seite(n)
789-869
Urheberrecht / Lizenzen
ISSN
0178-8051
eISSN
1432-2064
Page URI
https://pub.uni-bielefeld.de/record/2964896
Zitieren
Zhang X, Zhu R, Zhu X. Singular HJB equations with applications to KPZ on the real line. Probability Theory and Related Fields. 2022;183(3-4):789-869.
Zhang, X., Zhu, R., & Zhu, X. (2022). Singular HJB equations with applications to KPZ on the real line. Probability Theory and Related Fields, 183(3-4), 789-869. https://doi.org/10.1007/s00440-022-01137-w
Zhang, Xicheng, Zhu, Rongchan, and Zhu, Xiangchan. 2022. “Singular HJB equations with applications to KPZ on the real line”. Probability Theory and Related Fields 183 (3-4): 789-869.
Zhang, X., Zhu, R., and Zhu, X. (2022). Singular HJB equations with applications to KPZ on the real line. Probability Theory and Related Fields 183, 789-869.
Zhang, X., Zhu, R., & Zhu, X., 2022. Singular HJB equations with applications to KPZ on the real line. Probability Theory and Related Fields, 183(3-4), p 789-869.
X. Zhang, R. Zhu, and X. Zhu, “Singular HJB equations with applications to KPZ on the real line”, Probability Theory and Related Fields, vol. 183, 2022, pp. 789-869.
Zhang, X., Zhu, R., Zhu, X.: Singular HJB equations with applications to KPZ on the real line. Probability Theory and Related Fields. 183, 789-869 (2022).
Zhang, Xicheng, Zhu, Rongchan, and Zhu, Xiangchan. “Singular HJB equations with applications to KPZ on the real line”. Probability Theory and Related Fields 183.3-4 (2022): 789-869.
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