Probability and Statistics Seminar—— On the regularisation of reaction-diffusion equations by the Wight-Fisher white noise
报告人： Zhenyao Sun (Beijing Institute of Technology)
地点：Room 1114, Sciences Building No. 1
We will consider a family of 1-d reaction-diffusion equations perturbed by Wright-Fisher white noise, explicitly focusing on the equation.（公式见图1）
Traditionally, the weak uniqueness of this equation is only guaranteed when the drift is Lipschitz, i.e., α ≥ 1. However, recent work by Mueller-Mytnik-Ryzhik- 2021-CMP has shown that this weak uniqueness also holds when α ∈ [1 2, 1), provided that the initial value u0 has a compact interface. In this talk, we will go even further and show that the weak uniqueness of the equation holds for all α ∈ [0, 1) without any prior assumptions on the support of the initial value.
About the Speaker:
Your participation is warmly welcomed!