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.
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