Commutative C∗-algebras of Toeplitz operators and quantization on the unit disk
Commutative C∗-algebras of Toeplitz operators and quantization on the unit disk
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Toeplitz 算子的交换 C* 代数和单位圆盘上的量化
DOI：
10.1016/j.jfa.2005.11.015
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发表时间：
2006
影响因子：
1.7
通讯作者：
N. Vasilevski
中科院分区：
文献类型：
--
作者：
S. Grudsky;R. Quiroga;R. Quiroga;N. Vasilevski
我们研究一类 spde 解的样本路径规律，这些解在时间上是二阶的，并且包括随机波动方程。允许空间拉普拉斯算子的非整数幂。驱动噪声在时间和空间上是均匀的白噪声。继续 Dalang 和 Mueller 发起的工作（Electron. J. Probab. 8 (2003) 1），我们证明解属于分数 L2-Sobolev 空间。我们还证明了时间上的霍尔德连续性，因此，我们获得了时间和空间变量上的联合霍尔德连续性。我们的结论依赖于对 SPDE 严格公式中使用的随机积分性质的精确分析，正如 Dalang 和 Mueller 所介绍的那样。对于 Riesz 核给出的空间协方差，我们表明我们的结果是最优的。
We study the sample path regularity of the solutions of a class of spde's which are second order in time and that includes the stochastic wave equation. Non-integer powers of the spatial Laplacian are allowed. The driving noise is white in time and spatially homogeneous. Continuing with the work initiated in Dalang and Mueller (Electron. J. Probab. 8 (2003) 1), we prove that the solutions belong to a fractional L2-Sobolev space. We also prove Hölder continuity in time and therefore, we obtain joint Hölder continuity in the time and space variables. Our conclusions rely on a precise analysis of the properties of the stochastic integral used in the rigourous formulation of the spde, as introduced by Dalang and Mueller. For spatial covariances given by Riesz kernels, we show that our results are optimal.