Path Properties of Subdiffusion—A Martingale Approach
Path Properties of Subdiffusion—A Martingale Approach
复制标题
DOI：
10.1080/15326341003756379
复制
发表时间：
2010-04
影响因子：
0.7
通讯作者：
M. Magdziarz
中科院分区：
文献类型：
--
作者：
M. Magdziarz
在统计物理学中，次扩散过程构成了反常扩散模型家族中最相关的子类之一。这些过程的特征是与均方位移的经典布朗线性时间依赖关系有一定的幂规律偏差。在本文中，我们研究了次扩散的样本路径性质。对于次扩散模型的随机分析，我们提出了一种鞅方法。我们证明了轨道的鞅性质、Hölder连续性，并导出了大数定律。在重对数律下得到了次扩散的精确渐近性态。所得结果可用于识别实验数据中的亚扩散动力学类型。
In statistical physics, subdiffusion processes constitute one of the most relevant subclasses of the family of anomalous diffusion models. These processes are characterized by certain power-law deviations from the classical Brownian linear time dependence of the mean-squared displacement. In this article we study sample path properties of subdiffusion. We propose a martingale approach to the stochastic analysis of subdiffusion models. We verify the martingale property, Hölder continuity of the trajectories, and derive the law of large numbers. The precise asymptotic behavior of subdiffusion is obtained in the law of the iterated logarithm. The presented results may be applied to identify the type of subdiffusive dynamics in experimental data.