4 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 $$ \frac{\partial}{\partial t}u(t,x)=-(-Î)^{\fracα2}u (t,x)+\dot{W}(t,x),\ \ t> 0,\ \ x\in\RR, $$ where $-(-Î)^{\fracα{2…
Structure preservation and emergent dissipation in stochastic wave equations with transport noise
Chang Liu, Dejun Luo
We study nonlinear wave equations perturbed by transport noise acting either on the displacement or on the velocity. Such noise models random advection and, under suitable scaling…
Scaling Limit and Large Deviation for 3D Globally Modified Stochastic Navier-Stokes Equations with Transport Noise
Chang Liu, Dejun Luo
We consider the globally modified stochastic (hyperviscous) Navier-Stokes equations with transport noise on 3D torus. We first establish the existence and pathwise uniqueness of th…