Sticky-reflecting diffusion as a Wasserstein gradient flow
arxiv(2024)
摘要
In this paper we identify the Fokker-Planck equation for (reflected) Sticky
Brownian Motion as a Wasserstein gradient flow in the space of probability
measures. The driving functional is the relative entropy with respect to a
non-standard reference measure, the sum of an absolutely continuous interior
part plus a singular part supported on the boundary. Taking the small time-step
limit in a minimizing movement (JKO scheme) we prove existence of weak
solutions for the coupled system of PDEs satisfying in addition an Energy
Dissipation Inequality.
更多查看译文
AI 理解论文
溯源树
样例
生成溯源树,研究论文发展脉络
Chat Paper
正在生成论文摘要