4 papers
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\,,…
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 $$ \frac{\partial u (t,x)}{\partial t}=\frac{\partial^2 u (t,x)}{\partial x^2}+ σ(u (t,x))\dot{W}(t,x),\quad t> 0,\, x\in \mathbb{R}…
Sample path properties and small ball probabilities for stochastic fractional diffusion equations
Yuhui Guo, Jian Song, Ran Wang +1
We consider the following stochastic space-time fractional diffusion equation with vanishing initial condition:$$ \partial^β u(t, x)=- \left(-Δ\right)^{α/ 2} u(t, x)+ I_{0+}^γ\left…