论文标题
与多个目标的多个边界当地时代和相关的第一学期时间问题的联合分布
Joint distribution of multiple boundary local times and related first-passage time problems with multiple targets
论文作者
论文摘要
我们研究了具有限制域边界的不同子集的扩散粒子相遇的统计。与每个子集的相遇的特征是该子集上的边界本地时间。我们扩展了一种最近提出的方法，以表达粒子位置的关节概率密度及其多个边界本地时间，通过使用混合的罗宾边界条件满足扩散方程的常规传播器的多维拉环变换。在特定的间隔，圆形环和球形壳的特定情况下，可以明确倒置该表示形式以访问两个边界当地时间的统计数据。我们为间隔的情况提供了确切的解决方案及其概率解释，并在另外两种情况下勾勒出它们的推导。我们还获得了各种相关的第一学期时间的分布并讨论其应用。
We investigate the statistics of encounters of a diffusing particle with different subsets of the boundary of a confining domain. The encounters with each subset are characterized by the boundary local time on that subset. We extend a recently proposed approach to express the joint probability density of the particle position and of its multiple boundary local times via a multi-dimensional Laplace transform of the conventional propagator satisfying the diffusion equation with mixed Robin boundary conditions. In the particular cases of an interval, a circular annulus and a spherical shell, this representation can be explicitly inverted to access the statistics of two boundary local times. We provide the exact solutions and their probabilistic interpretation for the case of an interval and sketch their derivation for two other cases. We also obtain the distributions of various associated first-passage times and discuss their applications.
