论文标题
用于用椭圆形差异形式运算符的随机部分微分方程解决方案的空间二次变化
Spatial quadratic variations for the solution to a stochastic partial differential equation with elliptic divergence form operator
论文作者
论文摘要
我们引入了一个随机部分微分方程（SPDE），具有椭圆形算子的发散形式，具有可测量和有界系数，并由时空白噪声驱动。这样的SPDE可以用于由不同种类的材料和随机扰动组成的培养基的扩散现象的数学模型。我们表征了解决方案，并使用Stein-malliavin conculus表征了溶液，我们证明其近来的和重新归一化的空间二次变化的序列几乎满足了中心限制定理。特别关注操作员的系数是分段常数的有趣情况。
We introduce a stochastic partial differential equation (SPDE) with elliptic operator in divergence form, with measurable and bounded coefficients and driven by space-time white noise. Such SPDEs could be used in mathematical modelling of diffusion phenomena in medium consisting of different kinds of materials and undergoing stochastic perturbations. We characterize the solution and, using the Stein--Malliavin calculus, we prove that the sequence of its recentered and renormalized spatial quadratic variations satisfies an almost sure central limit theorem. Particular focus is given to the interesting case where the coefficients of the operator are piecewise constant.
