Chang Liu

Khinchin's and Chung's Laws of the Iterated Logarithm at Time Zero for the Linear Stochastic Fractional Diffusion Equation

We consider the linear stochastic fractional diffusion equation \begin{equation*} \partial^{\beta} u(t,x)=-\left(-\Delta\right)^{\alpha/2}u(t,x) +I_t^{\gamma}\bigl[\dot W(t,x)\bigr], \qquad t>0,\quad x\in\mathbb R^d, \end{equation*} with zero initial conditions, where $\alpha>0$, $\beta\in(0,2)$, and $\gamma\ge0$. The...