- Panqiu Xia
- Auburn University
- Date: Jan. 17, Wednesday, 2024
- Time: 10:00am -- 10:50am
- Host: Le Chen
- Room: Parker 326
- Abstract: In this talk, I will give a brief overview of the stochastic partial differential equations (SPDEs) and discuss previous results about the moment properties for SPDEs with linear growth. Next, I will focus on the sublinear SPDEs, namely, the diffusion coefficient exhibits sublinear growth at infinity. In case the diffusion coefficient \(\sigma(x) = \sqrt{x}\), the equation corresponds to the Lebesgue density to super-Brownian motion. For this equation, the matching upper and lower moment bounds are obtained via a combinatoric method. For more general cases, moment upper bounds have been derived by solving a Bihari–LaSalle type inequality. As applications, I will present some results regarding the estimation for tail probabilities and the almost sure asymptotics in space. This talk is based on several research projects collaborated with Le Chen, Yaozhong Hu, Michael Kouritzin, Xiong Wang, and Jiayu Zheng.