C. Lee

collaborators

6 papers

math.PR2026

Sharp moduli of continuity for Gaussian fields and stochastic PDEs via correlation bounds

Cheuk Yin Lee, Tianyi Zhang

Exact uniform and local moduli of continuity for anisotropic Gaussian random fields are established under a general framework based on correlation bounds for pairwise increments. T…

math.PR2025

Points of slow growth for parabolic SPDEs

Davar Khoshnevisan, Cheuk Yin Lee

Consider the stochastic PDE, $\partial_{t} u = \partial_{x}^{2} u + σ (u) W ˙$ on $R_{+} \times R$ , subject to $u (0) \equiv 1$ , where $W ˙$ denotes space-time white noi…

math.PR2025

Uniform dimension theorems for parabolic SPDEs

Davar Khoshnevisan, Cheuk Yin Lee, Fei Pu +1

Consider the following $p$ -dimensional system of ItÃ´ 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\…

math.PR2025

On the passage times of self-similar Gaussian processes on curved boundaries

Davar Khoshnevisan, Cheuk Yin Lee

Let $T_{c, I^^{2}}$ denote the smallest $t \geq 1$ that a continuous, self-similar Gaussian process with self-similarity index $I^\pm > 0$ moves at least $\pm c t^{2}$ units. We prove that: (i)…

math.PR2025

Hitting probabilities, thermal capacity, and Hausdorff dimension results for the Brownian sheet

Cheuk Yin Lee, Yimin Xiao

Let $W = {W (t) : t \in R_{+}^{N}}$ be an $(N, d)$ -Brownian sheet and let $E \subset (0, \infty)^{N}$ and $F \subset R^{d}$ be compact sets. We prove a necessary and suff…

math.PR2025

Local times of anisotropic Gaussian random fields and stochastic heat equation

Cheuk Yin Lee, Yimin Xiao

We study the local times of a large class of Gaussian random fields satisfying strong local nondeterminism with respect to an anisotropic metric. We establish moment estimates and…