各向同性Pearson随机游走的渐近行为
Asymptotic Behaviour for Isotropic Pearson Random Walks
浏览论文内容
中文总结 AI 辅助
本文研究维度趋于无穷时各向同性Pearson随机游走的渐近行为，拓展至步数与步长均依赖维度的情况，相关结果可用于近似经典Pearson随机游走的分布。
中文摘要 AI 辅助
在Pearson随机游走中，第i步的方向是d维球面上均匀分布的随机变量，步长为非负随机变量。本文将在一般框架下研究当维度d趋于无穷时Pearson随机游走的渐近行为，还会在步数和步长均依赖于维度的更一般框架下探究相同收敛结果。本文结果可用于近似一些经典Pearson随机游走的分布，例如Dirichlet情形下的分布。
英文摘要
In the Pearson random walk the direction of the i-th step is a random variable uniformly distributed on the d-dimensional sphere, and its length is a non-negative random variable. In a general framework, we are going to study the asymptotic behaviour of the Pearson random walks when the dimension d goes to infinity. Further, we investigate the same convergence result in a more general framework, where both the number and the lengths of the steps depend on the dimension. The results in the present paper can be applied to approximate the distribution of some classical Pearson random walk, for example, in the Dirichlet case.
发表机构
- Università dell’Insubria（因苏布里亚大学）
机构由 AI 辅助整理，请以论文原文为准。
