Yimin Xiao

collaborators

5 papers

math.PR2026

Strassen's local law of the iterated logarithm for the generalized fractional Brownian motion

Ran Wang, Yimin Xiao

Let $X := {X (t)}_{t \geq 0}$ be a generalized fractional Brownian motion given by $$ \{X(t)\}_{t\ge0}\overset{d}{=}\left\{ \int_{\mathbb R} \left((t-u)_+^Î±-(-u)_+^Î± \right) |u|^{-Î³…

math.PR2026

Polarity of points for Gaussian random fields in critical dimension

Youssef Hakiki, Cheuk Yin Lee, Yimin Xiao

We study the property of hitting points for a class of $R^{d}$ -valued continuous Gaussian random fields on $R^{N}$ with stationary increments, i.i.d. coordinates, and…

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

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}+ Ï(u (t,x))\dot{W}(t,x),\quad t> 0,\, x\in \mathbb{R…