Singular HJB equations with applications to KPZ on the real line

2020/07/14 by Xicheng Zhang, Zhang, Xicheng, Rongchan Zhu +3 · 2 citations
Economics, Econometrics and Finance · Mathematics · #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Probability (math.PR) #Stochastic processes and financial applications

paper · pdf · doi:10.48550/arxiv.2007.06783

openalex publication_date 2020/07/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

This paper is devoted to studying the Hamilton-Jacobi-Bellman equations with distribution-valued coefficients, which is not well-defined in the classical sense and shall be understood by using paracontrolled distribution method introduced in \citeGIP15. By a new characterization of weighted Hölder space and Zvonkin's transformation we prove some new a priori estimates, and therefore, establish the global well-posedness for singular HJB equations. As an application, the global well-posedness for KPZ equations on the real line in polynomial weighted Hölder spaces is obtained without using Cole-Hopf's transformation. In particular, we solve the conjecture posed in \cite[Remark 1.1]PR18.

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