标题： 随机抛物型算子振荡系数解的渐近分解 显示英文标题

标题： Asymptotic decomposition of solutions to random parabolic operators with oscillating coefficients

摘要： 我们考虑具有快速振荡系数的散度形式二阶抛物型算子的柯西问题，这些系数在空间变量上是周期性的，在时间上是随机平稳遍历的。 如[25]和[13]中所证明的，在这种情况下，均质化算子是确定性的。 我们得到了解的渐近展开式的主导项，这些项是确定性函数，并表明解与所述主导项之间适当归一化的差收敛于某个SPDE的解。 显示英文摘要

摘要： We consider Cauchy problem for a divergence form second order parabolic operator with rapidly oscillating coefficients that are periodic in spatial variable and random stationary ergodic in time. As was proved in [25] and [13] in this case the homogenized operator is deterministic. We obtain the leading terms of the asymptotic expansion of the solution , these terms being deterministic functions, and show that a properly renormalized difference between the solution and the said leading terms converges to a solution of some SPDE.