5 papers
Khinchin's and Chung's Laws of the Iterated Logarithm at Time Zero for the Linear Stochastic Fractional Diffusion Equation
Chang Liu, Ran Wang
We consider the linear stochastic fractional diffusion equation \begin{equation*} \partial^β u(t,x)=-\left(-Δ\right)^{α/2}u(t,x) +I_t^γ\bigl[\dot W(t,x)\bigr], \qquad t>0,\quad x\i…
Growth rates for the Hölder coefficients of the linear stochastic fractional heat equation with rough dependence in space
Chang Liu, Bin Qian, Ran Wang
We study the linear stochastic fractional heat equation $$ \frac{\partial}{\partial t}u(t,x)=-(-Δ)^{\fracα2}u (t,x)+\dot{W}(t,x),\ \ t> 0,\ \ x\in\RR, $$ where …
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 $$ \frac{\partial u (t,x)}{\partial t}=\frac{\partial^2 u (t,x)}{\partial x^2}+ σ(u (t,x))\dot{W}(t,x),\quad t> 0,\, x\in \mathbb{R}…
Strassen's local law of the iterated logarithm for the generalized fractional Brownian motion
Ran Wang, Yimin Xiao
Let be a generalized fractional Brownian motion given by $$ \{X(t)\}_{t\ge0}\overset{d}{=}\left\{ \int_{\mathbb R} \left((t-u)_+^α-(-u)_+^α \right) |u|^{-γ/2}…
Lower classes and Chung's LILs of the fractional integrated generalized fractional Brownian motion
Mengjie Lyu, Min Wang, Ran Wang
Let be the generalized fractional Brownian motion introduced by Pang and Taqqu (2019): \begin{align*} \{X(t)\}_{t\ge0}\overset{d}{=}&\left\{ \int_{\mathbb…