29 citations · 75 across the 24 of their papers we have counts for
26 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…
The ergodic theory of SPDEs in a weak-noise regime
Mathew Joseph, Davar Khoshnevisan, Kunwoo Kim +1
Consider a parabolic SPDE \[ \partial_t u = Δu + σ(u)η, \] on , where is a centered, generalized Gaussian noise with $\text{Cov}[η(t\,,x)\,,η(s\…
An Invariance Principle for some Reaction-Diffusion Equations with a Multiplicative Random Source
Davar Khoshnevisan, Kunwoo Kim, Carl Mueller
We establish a notion of universality for the parabolic Anderson model via an invariance principle for a wide family of parabolic stochastic partial differential equations. We then…
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…
Small-ball constants, and exceptional flat points of SPDEs
Davar Khoshnevisan, Kunwoo Kim, Carl Mueller
We study small-ball probabilities for the stochastic heat equation with multiplicative noise in the moderate-deviations regime. We prove the existence of a small-ball constant and…