论文标题
条件韦纳过程作为非线性：对动态的严格概率分析
Conditioned Weiner Processes as Nonlinearities: A Rigorous Probabilistic Analysis of Dynamics
论文作者
论文摘要
我们研究了一个韦纳过程，该过程有条件通过一组有限的点，并考虑通过从该过程中迭代样品路径产生的动力学。使用拓扑技术，我们能够表征全局动力学并推断不变集的存在，结构和近似位置。最重要的是，我们计算出这种表征正确的概率。这项工作本质上是概率的，旨在为动态系统的统计分析提供理论基础，该系统只能通过有限样本查询。
We study a Weiner process that is conditioned to pass through a finite set of points and consider the dynamics generated by iterating a sample path from this process. Using topological techniques we are able to characterize the global dynamics and deduce the existence, structure and approximate location of invariant sets. Most importantly, we compute the probability that this characterization is correct. This work is probabilistic in nature and intended to provide a theoretical foundation for the statistical analysis of dynamical systems which can only be queried via finite samples.
