Author

Ran Wang

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Preprint Oct 2026

Local Linearization and Exact Oscillations for the Nonlinear Stochastic Heat Equation with Spatially Rough Noise

Consider the one-dimensional nonlinear stochastic heat equation $$ \frac{\partial u(t,x)}{\partial t} = \frac{\partial^2 u(t,x)}{\partial x^2} + \sigma(u(t,x))\dot W(t,x), \qquad t>0,\ x\in\mathbb R, $$ where $\dot W$ is a Gaussian noise that is white in time and fractional in space with Hurst parameter $H\in(1/4,1/2)$...

Bin Qian, Meng-Xin Tong, Ran Wang et al. · 0 citations

Preprint Aug 2026

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...

Chang Liu, Ran Wang · 0 citations