论文标题
轨道的尺寸和形状
Size and shape of tracked Brownian bridges
论文作者
论文摘要
我们研究了通过不规则地跟踪二维布朗桥获得的典型尺寸和形状。跟踪过程包括在有限的时间间隔内观察非均匀泊松过程的到达时间的路径位置。这个观察过程的时间变化的时间是跟踪策略。通过分析跟踪点的回旋张量，我们证明了两个定理，它们将跟踪策略与平均回旋半径和非球面相关联 - 衡量了点集的非球面。跟踪行为可以解释为观察过程，也可以将其沉积时间腐烂的“证据”（例如气味，环境干扰或疾病颗粒）解释为。我们介绍了不同策略的示例，并通过模拟改变跟踪点总数的影响。
We investigate the typical sizes and shapes of sets of points obtained by irregularly tracking two-dimensional Brownian bridges. The tracking process consists of observing the path location at the arrival times of a non-homogeneous Poisson process on a finite time interval. The time varying intensity of this observation process is the tracking strategy. By analysing the gyration tensor of tracked points we prove two theorems which relate the tracking strategy to the average gyration radius, and to the asphericity -- a measure of how non-spherical the point set is. The act of tracking may be interpreted either as a process of observation, or as process of depositing time decaying "evidence" such as scent, environmental disturbance, or disease particles. We present examples of different strategies, and explore by simulation the effects of varying the total number of tracking points.
