3 citations · 4 across the 8 of their papers we have counts for
9 papers
Limit theorems for the one-dimensional parabolic Anderson model with white noise potential
Kunwoo Kim, Uijun Kim, Jaeyun Yi
We consider the parabolic Anderson model on with , where is a spatial white noise. We study…
Instantaneous shrinking of supports for stochastic PDEs
Beom-Seok Han, Kunwoo Kim, Jaeyun Yi
We study instantaneous shrinking of supports for nonnegative solutions of the stochastic partial differential equation \[ \partial_t u=a(t,x)\,\partial_x^2 u + b(t,x)\,\partial_x u…
On the support of solutions to nonlinear stochastic heat equations
Beom-Seok Han, Kunwoo Kim, Jaeyun Yi
We investigate the strict positivity and the compact support property of solutions to the one-dimensional nonlinear stochastic heat equation: $$\partial_t u(t,x) = \frac{1}{2}\part…
-regularity theory for the stochastic reaction-diffusion equation with super-linear multiplicative noise and strong dissipativity
Beom-Seok Han, Jaeyun Yi
We study the existence, uniqueness, and regularity of the solution to the stochastic reaction-diffusion equation (SRDE) with colored noise : $$ \partial_t u = a^{ij}u_{x^i…
Fractal geometry of the PAM in 2D and 3D with white noise potential
Promit Ghosal, Jaeyun Yi
We study the parabolic Anderson model (PAM) \begin{equation} {\partial \over \partial t}u(t,x) =\frac{1}{2}Δu(t,x) + u(t,x)ξ(x), \quad t>0, x\in \mathbb{R}^d, \quad \text{and} \qua…
The compact support property for solutions to the stochastic partial differential equations with colored noise
Beom-Seok Han, Kunwoo Kim, Jaeyun Yi
We study the compact support property for solutions of the following stochastic partial differential equations: $$\partial_t u = a^{ij}u_{x^ix^j}(t,x)+b^{i}u_{x^i}(t,x)+cu+h(t,x,u(…
Fractal Geometry of the Valleys of the Parabolic Anderson Equation
Promit Ghosal, Jaeyun Yi
We study the macroscopic fractal properties of the deep valleys of the solution of the -dimensional parabolic Anderson equation $${\partial \over \partial t}u(t,x) =\frac{1}…
Macroscopic multi-fractality of Gaussian random fields and linear SPDEs with colored noise
Jaeyun Yi
We consider the linear stochastic heat and wave equations with generalized Gaussian noise that is white in time and spatially correlated. Under the assumption that the homogeneous…
Limit theorems for time-dependent averages of nonlinear stochastic heat equations
Kunwoo Kim, Jaeyun Yi
We study limit theorems for time-dependent averages of the form , as , where and is th…