Set Estimation from Reflected Brownian Motion
研究了如何从反射布朗运动的轨迹估计一个紧集及其边界，建立了估计量的一致性和收敛速度，为基于追踪数据估计动物活动范围提供了理论基础。
Summary We study the problem of estimating a compact set S⊂Rd from a trajectory of a reflected Brownian motion in S with reflections on the boundary of S. We establish consistency and rates of convergence for various estimators of S and its boundary. This problem has relevant applications in ecology in estimating the home range of an animal on the basis of tracking data. There are a variety of studies on the habitat of animals that employ the notion of home range. The paper offers theoretical foundations for a new methodology that, under fairly unrestrictive shape assumptions, allows us to find flexible regions close to reality. The theoretical findings are illustrated on simulated and real data examples.