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<p>We prove differentiability of the effective Lagrangian for continuous time multidimensional directed variational problems in random dynamic environments with positive dependence range in time. This implies that limiting fundamental solutions in the associated homogenization problems for HJB equations are classical.</p>

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Differentiability of the effective Lagrangian for Hamilton–Jacobi–Bellman equations in dynamic random environments

  • 期刊论文

  • 发表日期：

    2025年6月14日

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  • Yuri Bakhtin,
  • Douglas Dow

摘要

We prove differentiability of the effective Lagrangian for continuous time multidimensional directed variational problems in random dynamic environments with positive dependence range in time. This implies that limiting fundamental solutions in the associated homogenization problems for HJB equations are classical.