Viscosity Solutions to HJB Equations with Hölder Continuous Coefficients

Jianrui Li (), Jinghai Shao () and Hui Zhao ()
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Jianrui Li: Tianjin University
Jinghai Shao: Tianjin University
Hui Zhao: Nankai University

Journal of Optimization Theory and Applications, 2025, vol. 205, issue 3, No 8, 15 pages

Abstract: Abstract This work studies the optimal control problem for diffusion processes with Hölder continuous coefficients. Based on Meyer–Tanaka’s formula, we establish an estimate on the local times of controlled diffusion processes, which enables us to provide a new estimate on the regularity of the value function. Then, the value function can be characterized as a unique viscosity solution of certain HJB equation.

Keywords: Hölder continuous; Viscosity solutions; HJB equations; Comparison principle; 93E20; 60J60; 35F50 (search for similar items in EconPapers)
Date: 2025
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DOI: 10.1007/s10957-025-02665-w

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