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<p>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.</p>

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Viscosity Solutions to HJB Equations with Hölder Continuous Coefficients

  • 期刊论文

  • 发表日期：

    2025年4月17日

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  • Jianrui Li,
  • Jinghai Shao,
  • Hui Zhao

摘要

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.