On estimating the derivatives of symmetric diffusions in stationary random environment, with applications to ∇ϕ interface model
On estimating the derivatives of symmetric diffusions in stationary random environment, with applications to ∇ϕ interface model
复制标题
估计平稳随机环境中对称扩散的导数及其在 ∇ψ 接口模型中的应用
DOI：
--
复制
发表时间：
2005
期刊：
影响因子：
--
通讯作者：
J. Deuschel
中科院分区：
文献类型：
--
作者：
Thierry Delmotte;J. Deuschel
摘要。我们考虑在空间和时间上都是平稳的随机环境下，在空间和时间上都是对称的、均匀的椭圆系数的随机环境下，在l - d上的扩散或随机行走。我们证明了这种扩散的退火核的二阶空间导数和时间导数的存在性和Hölder连续性，并给出了这些导数的估计。在随机漫步的情况下，这些估计被应用于Ginzburg-Landau∇φ接口模型。
Abstract.We consider diffusions on ℝd or random walks on ℤd in a random environment which is stationary in space and in time and with symmetric and uniformly elliptic coefficients. We show existence and Hölder continuity of second space derivatives and time derivatives for the annealed kernels of such diffusions and give estimates for these derivatives. In the case of random walks, these estimates are applied to the Ginzburg-Landau ∇ϕ interface model.