- Stochastics Seminar
- Thursday, September 12, 2019 - 3:05pm for 1 hour (actually 50 minutes)
- Skiles 006
- Le Chen – Emory University
- Konstantin Tikhomirov
In this talk, I will present some recent works on the stochastic heat equation with a general multiplicative Gaussian noise that is white in time and colored in space, including space-time white noise. We will show both regularity and strict positivity of the densities of the solution. The difficulties of this study include rough initial conditions, degenerate diffusion coefficient, and weakest possible assumptions on the correlation function of the noise. In particular, our results cover the parabolic Anderson model starting from a Dirac delta initial measure. The spatial one-dimensional case is based on the joint-work with Yaozhong Hu and David Nualart  and the higher dimension case with Jingyu Huang .
 L. Chen, Y. Hu and D. Nualart, Regularity and strict positivity of densities for the nonlinear stochastic heat equation. Memoirs of American Mathematical Society, accepted in 2018, to appear in 2020.
 L. Chen, J. Huang, Regularity and strict positivity of densities for the stochastic heat equation on Rd. Preprint at arXiv:1902.02382.