论文标题
部分可观测时空混沌系统的无模型预测
Geodesic Lévy flights and expected stopping time for random searches
论文作者
论文摘要
我们对Applebaum-Ettrade构建的无限发电机进行分析描述，用于在一系列封闭的Riemannian歧管上为Lévy飞行而建造的，包括所有负面弯曲的歧管，平坦的圆环和球体。然后，使用我们对无穷小发电机的新发现的理解，获得了相关半群的各种特性以及基于莱维飞行的随机搜索（也称为狭窄的捕获问题）的预期停止时间的渐近学。我们的研究还涉及生物学领域的Lévy飞行觅食假设，因为我们通过使用Lévy飞行随机搜索来计算寻找小目标的预期时间。在[Arxiv：2209.12425]中，对布朗运动进行了类似的计算。
We give an analytic description for the infinitesimal generator constructed by Applebaum-Estrade for Lévy flights on a broad class of closed Riemannian manifolds including all negatively-curved manifolds, the flat torus and the sphere. Various properties of the associated semigroup and the asymptotics of the expected stopping time for Lévy flight based random searches for small targets, also known as the narrow capture problem, are then obtained using our newfound understanding of the infinitesimal generator. Our study also relates to the Lévy flight foraging hypothesis in the field of biology as we compute the expected time for finding a small target by using the Lévy flight random search. A similar calculation for Brownian motion on surfaces was done in [arXiv:2209.12425].
