- Panqiu Xia
- Auburn University
- Date: Oct. 11, Tuesday, 2022
- Time: 2:30pm -- 3:30pm
- Room: Parker 326
- Abstract: The super-Brownian motion (sBm), or Dawson-Watanabe superprocess, is a typical example of the measure-valued Markov processes. In the spatial dimensional one, the sBm, viewed as a measure on R, is absolutely continuous with respect to the Lebesgue measure. Moreover, the density of this measure is the unique solution to the stochastic heat equation with the diffusion coefficient taking the form of square root. This equation is one of the most important example of the stochastic partial differential equation with non-Lipschitz coefficients. In this talk, I will first give a brief introduction to sBm's and then show some recent results about moment formula and large time and high order moment asymptotics of sBm's.