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math.PR2026
Local Linearization and Exact Oscillations for the Nonlinear Stochastic Heat Equation with Spatially Rough Noise
Bin Qian, Mengxin Tong, Ran Wang +1
Consider the one-dimensional 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), \qquad t>0,\…
math.PR2026
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…