空间图上过程的外推与抽样
Extrapolation and sampling for processes on spatial graphs
摘要：
本文研究定义在时域上的过程，其结构为定向空间图（或度量图，或定向分支1-流形）。例如，此设置可用于涉及分支方案的预测模型。对于这些过程，考虑到图的拓扑结构的频谱退化的概念被引入。本文给出了由单支观测值进行外推和恢复的唯一性的充分条件。这也意味着分支过程的采样定理的模拟，即，从一组等距样本以及从一组来自单个分支的等距样本中恢复的标准。
英文摘要：
The paper studies processes defined on time domains structured as oriented spatial graphs (or metric graphs, or oriented branched 1-manifolds). This setting can be used, for example, for forecasting models involving branching scenarios. For these processes, a notion of the spectrum degeneracy that takes into account the topology of the graph is introduced. The paper suggests sufficient conditions of uniqueness of extrapolation and recovery from the observations on a single branch. This also implies an analog of sampling theorem for branching processes, i.e., criterions of their recovery from a set of equidistant samples, as well as from a set of equidistant samples from a single branch.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
