2 citations · 3 across the 18 of their papers we have counts for
20 papers
Sharp regularity and small ball probabilities for the stochastic heat equation on bounded domains
Jingwu Hu, Cheuk Yin Lee
We consider the stochastic heat equation on a bounded Lipschitz domain with zero Dirichlet boundary condition and zero initial condit…
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…
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…
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)) + σ(u(t\,,…
Propagation of Singularities for the Damped Stochastic Klein-Gordon Equation
Hongyi Chen, Cheuk Yin Lee
For the dimensional damped stochastic Klein-Gordon equation, we show that random singularities associated with the law of the iterated logarithm exist and propogate in the sa…
On the spatio-temporal increments of nonlinear parabolic SPDEs and the open KPZ equation
Jingwu Hu, Cheuk Yin Lee
We study spatio-temporal increments of the solutions to nonlinear parabolic SPDEs on a bounded interval with Dirichlet, Neumann, or Robin boundary conditions. We identify the exact…
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) If…
Hitting probabilities, thermal capacity, and Hausdorff dimension results for the Brownian sheet
Cheuk Yin Lee, Yimin Xiao
Let be an -Brownian sheet and let and be compact sets. We prove a necessary and suff…
Growth rate of liquidity provider's wealth in G3Ms
Cheuk Yin Lee, Shen-Ning Tung, Tai-Ho Wang
We study how trading fees and continuous-time arbitrage affect the profitability of liquidity providers (LPs) in Geometric Mean Market Makers (G3Ms). We use stochastic reflected di…
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…
Polarity of points for systems of nonlinear stochastic heat equations in the critical dimension
Cheuk Yin Lee, Yimin Xiao
Let be the solution to the systems of nonlinear stochastic heat equations \[ \begin{split} \frac{\partial}{\partial t} u(t, x) &= \frac{\p…
Hitting probabilities of Gaussian random fields and collision of eigenvalues of random matrices
Cheuk Yin Lee, Jian Song, Yimin Xiao +1
Let be a centered Gaussian random field with values in satisfying certain conditions and let be a Borel set.…
Chung-type law of the iterated logarithm and exact moduli of continuity for a class of anisotropic Gaussian random fields
Cheuk Yin Lee, Yimin Xiao
We establish a Chung-type law of the iterated logarithm and the exact local and uniform moduli of continuity for a large class of anisotropic Gaussian random fields with a harmoniz…
Local nondeterminism and local times of the stochastic wave equation driven by fractional-colored noise
Cheuk Yin Lee
We investigate the existence and regularity of the local times of the solution to a linear system of stochastic wave equations driven by a Gaussian noise that is fractional in time…
The Hausdorff measure of the range and level sets of Gaussian random fields with sectorial local nondeterminism
Cheuk Yin Lee
We determine the exact Hausdorff measure functions for the range and level sets of a class of Gaussian random fields satisfying sectorial local nondeterminism and other assumptions…
The Multiple Points of Fractional Brownian Motion
Mark Landry, Cheuk Yin Lee, Paige Pearcy
Nils Tongring (1987) proved sufficient conditions for a compact set to contain -tuple points of a Brownian motion. In this paper, we extend these findings to the fractional Brow…
Propagation of Singularities for the Stochastic Wave Equation
Cheuk Yin Lee, Yimin Xiao
We study the existence and propagation of singularities of the solution to a one-dimensional linear stochastic wave equation driven by an additive Gaussian noise that is white in t…
Multiple Points of Gaussian Random Fields
Robert C. Dalang, Cheuk Yin Lee, Carl Mueller +1
This paper is concerned with the existence of multiple points of Gaussian random fields. Under the framework of Dalang et al. (2017), we prove that, for a wide class of Gaussian ra…
Local Nondeterminism and the Exact Modulus of Continuity for Stochastic Wave Equation
Cheuk Yin Lee, Yimin Xiao
We consider the linear stochastic wave equation driven by a Gaussian noise. We show that the solution satisfies a certain form of strong local nondeterminism and we use this proper…