8 papers
On the slow points of fractional Brownian motion
Davar Khoshnevisan, Cheuk Yin Lee
Esser and Loosveldt have recently resolved a long-standing open problem in the folklore by proving that fractional Brownian motion (fBm) has slow points in the sense of Kahane, fol…
On the local well-posedness of randomly forced reaction-diffusion equations with initial data and a superlinear reaction term
Mohammud Foondun, Davar Khoshnevisan, Eulalia Nualart
We consider a parabolic stochastic partial differential equation (SPDE) on that is forced with multiplicative space-time white noise with a bounded and Lipschitz diffusio…
The ergodic theory of SPDEs in a weak-noise regime
Mathew Joseph, Davar Khoshnevisan, Kunwoo Kim +1
Consider a parabolic SPDE \[ \partial_t u = Îu + Ï(u)η, \] on , where is a centered, generalized Gaussian noise with $\text{Cov}[η(t\,,x)\,…
Points of slow growth for parabolic SPDEs
Davar Khoshnevisan, Cheuk Yin Lee
Consider the stochastic PDE, on , subject to , where denotes space-time white noi…
Uniform dimension theorems for parabolic SPDEs
Davar Khoshnevisan, Cheuk Yin Lee, Fei Pu +1
Consider the following -dimensional system of Itô type stochastic PDEs, \begin{align*}\left[\begin{aligned} &\partial_t u(t\,,x) = \partial^2_x u(t\,,x) + b(u(t\,,x)) + Ï(u(t\…
On the passage times of self-similar Gaussian processes on curved boundaries
Davar Khoshnevisan, Cheuk Yin Lee
Let denote the smallest that a continuous, self-similar Gaussian process with self-similarity index moves at least units. We prove that: (i)…