Approximating dynamics of a singularly perturbed stochastic wave   equation with a random dynamical boundary condition
  This work is concerned with a singularly perturbed stochastic nonlinear wave equation with a random dynamical boundary condition. A splitting skill is used to derive the approximating equation of the system in the sense of probability distribution, when the singular perturbation parameter is sufficiently small. The approximating equation is a stochastic parabolic equation when the power exponent of singular perturbation parameter is in $[1/2, 1)$, but a deterministic hyperbolic (wave) equation when the power exponent is in $(1, +\infty)$. 
Guanggan Chen, Jinqiao Duan, Jian Zhang
math.AP math.PR