Yimin Xiao

activity

20242026

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3 papers · 1 filter

math.PR2025

Uniform dimension theorems for parabolic SPDEs

Davar Khoshnevisan, Cheuk Yin Lee, Fei Pu +1

Consider the following $p$ -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\,,…

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

Temporal regularity for the stochastic heat equation with rough dependence in space

Bin Qian, Min Wang, Ran Wang +1

Consider the nonlinear stochastic heat equation $$ \frac{\partial u (t,x)}{\partial t}=\frac{\partial^2 u (t,x)}{\partial x^2}+ σ(u (t,x))\dot{W}(t,x),\quad t> 0,\, x\in \mathbb{R}…