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Singular HJB equations with applications to KPZ on the real line.
- Source :
-
Probability Theory & Related Fields . Aug2022, Vol. 183 Issue 3/4, p789-869. 81p. - Publication Year :
- 2022
-
Abstract
- 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. [ABSTRACT FROM AUTHOR]
- Subjects :
- *EQUATIONS
*BACKLUND transformations
*SINGULAR integrals
*MATHEMATICS
Subjects
Details
- Language :
- English
- ISSN :
- 01788051
- Volume :
- 183
- Issue :
- 3/4
- Database :
- Academic Search Index
- Journal :
- Probability Theory & Related Fields
- Publication Type :
- Academic Journal
- Accession number :
- 158019994
- Full Text :
- https://doi.org/10.1007/s00440-022-01137-w