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<p>We derive the nonlinear stochastic Fokker-Planck equation from stochastic particle systems with individual and environmental noises via relative entropy method, with pathwise quantitative bounds. Moreover, we prove the existence of a unique strong solution to the associated Fokker-Planck equation. Our proof is based on tools from PDE analysis, stochastic analysis, functional inequalities, and also we use the dissipation of entropy which provides some bound on the Fisher information of the particle system. The approach applies to repulsive and attractive kernels.</p>

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Pathwise quantitative particle approximation of nonlinear stochastic Fokker-Planck equations via relative entropy

  • 期刊论文

  • 发表日期：

    2026年4月29日

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  • Christian Olivera,
  • Alexandre B. de Souza

摘要

We derive the nonlinear stochastic Fokker-Planck equation from stochastic particle systems with individual and environmental noises via relative entropy method, with pathwise quantitative bounds. Moreover, we prove the existence of a unique strong solution to the associated Fokker-Planck equation. Our proof is based on tools from PDE analysis, stochastic analysis, functional inequalities, and also we use the dissipation of entropy which provides some bound on the Fisher information of the particle system. The approach applies to repulsive and attractive kernels.