Limit theorems for time-dependent averages of nonlinear stochastic heat equations

Kunwoo Kim, Jaeyun Yi

We study limit theorems for time-dependent averages of the form $X_t:=\frac{1}{2L(t)}{\int }_{-L(t)}^{L(t)}u(t,x)dx$, as $t\to \infty$, where $L(t)=\exp (\lambda t)$ and $u(t,x)$ is th…