6 papers
Strassen's local law of the iterated logarithm for the generalized fractional Brownian motion
Ran Wang, Yimin Xiao
Let be a generalized fractional Brownian motion given by $$ \{X(t)\}_{t\ge0}\overset{d}{=}\left\{ \int_{\mathbb R} \left((t-u)_+^α-(-u)_+^α \right) |u|^{-γ…
Polarity of points for Gaussian random fields in critical dimension
Youssef Hakiki, Cheuk Yin Lee, Yimin Xiao
We study the property of hitting points for a class of -valued continuous Gaussian random fields on with stationary increments, i.i.d. coordinates, and…
Uniform dimension theorems for parabolic SPDEs
Davar Khoshnevisan, Cheuk Yin Lee, Fei Pu +1
Consider the following -dimensional system of Itô type stochastic PDEs, \begin{align*}\left[\begin{aligned} &\partial_t u(t\,,x) = \partial^2_x u(t\,,x) + b(u(t\,,x)) + Ï(u(t\…
Hitting probabilities, thermal capacity, and Hausdorff dimension results for the Brownian sheet
Cheuk Yin Lee, Yimin Xiao
Let be an -Brownian sheet and let and be compact sets. We prove a necessary and suff…
Temporal regularity for the stochastic heat equation with rough dependence in space
Bin Qian, Min Wang, Ran Wang +1
Consider the nonlinear stochastic heat equation $$ \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…
Sample path properties and small ball probabilities for stochastic fractional diffusion equations
Yuhui Guo, Jian Song, Ran Wang +1
We consider the following stochastic space-time fractional diffusion equation with vanishing initial condition:$$ \partial^β u(t, x)=- \left(-Î\right)^{α/ 2} u(t, x)+ I_{0+}^γ\…