相关论文: Set estimation from reflected Brownian motion
We quantify the asymptotic behaviour of multidimensional drifltess diffusions in domains unbounded in a single direction, with asymptotically normal reflections from the boundary. We identify the critical growth/contraction rates of the…
Shape estimation and object reconstruction are common problems in image analysis. Mathematically, viewing objects in the image plane as random sets reduces the problem of shape estimation to inference about sets. Currently existing…
The home range of a specific animal describes the geographic area where this individual spends most of the time while carrying out its usual activities (eating, resting, reproduction, ...). Although a well-established definition of this…
We define and prove the existence of a fractional Brownian motion indexed by a collection of closed subsets of a measure space. This process is a generalization of the set-indexed Brownian motion, when the condition of independance is…
A theory is provided for the estimation of home ranges of animals from the standard mark-recapture technique in which data are collected by capturing, tagging and recapturing the animals. The theoretical tool used is the Fokker-Planck…
Consider a generic triangle in the upper half of the complex plane with one side on the real line. This paper presents a tailored construction of a discrete random walk whose continuum limit is a Brownian motion in the triangle, reflected…
We study the recovery of one-dimensional semipermeable barriers for a stochastic process in a planar domain. The considered process acts like Brownian motion when away from the barriers and is reflected upon contact until a sufficient but…
We systematically develop general tools to apply Fukushima's absolute continuity condition. These tools comprise methods to obtain a Hunt process on a locally compact separable metric state space whose transition function has a density…
We construct obliquely reflected Brownian motions in all bounded simply connected planar domains, including non-smooth domains, with general reflection vector fields on the boundary. Conformal mappings and excursion theory are our main…
The accuracy assessment of remote-sensing derived built-up land data represents a specific case of binary map comparison, where class imbalance varies considerably across rural-urban trajectories. Thus, local accuracy characterization of…
We investigate a general class of models for swarming/self-collective behaviour in domains with boundaries. The model is expressed as a stochastic system of interacting particles subject to both reflecting boundary condition and common…
We use Stein's method to obtain a bound on the distance between scaled $p$-dimensional random walks and a $p$-dimensional (correlated) Brownian Motion. We consider dependence schemes including those in which the summands in scaled sums are…
In this paper, we propose numerical methods for computing the boundary local time of reflecting Brownian motion (RBM) in R3 and its use in the probabilistic representation of the solution of the Laplace equation with the Neumann boundary…
Predicting the future motion of vehicles has been studied using various techniques, including stochastic policies, generative models, and regression. Recent work has shown that classification over a trajectory set, which approximates…
We give necessary and sufficient conditions for the stationary density of semimartingale reflected Brownian motion in a wedge to be written as a finite sum of terms of exponential product form. Relying on geometric ideas reminiscent of the…
Experimental methods based on single particle tracking (SPT) are being increasingly employed in the physical and biological sciences, where nanoscale objects are visualized with high temporal and spatial resolution. SPT can probe…
In the three decades since its introduction, resource selection analysis (RSA) has become a widespread method for analyzing spatial patterns of animal relocations obtained from telemetry studies. Recently, mechanistic home range models have…
In a previous paper, we established strong existence and uniqueness for a reflected diffusion $(X,S)$ with values in $\bar D\times \mathbbm{R}^p$, solving the following pair of stochastic differential equations: $$ dX_t = \sigma(X_t)dB_t +…
Fractional Brownian motion is a Gaussian stochastic process with stationary, long-time correlated increments and is frequently used to model anomalous diffusion processes. We study numerically fractional Brownian motion confined to a finite…
Estimating the geographical range of a species from sparse observations is a challenging and important geospatial prediction problem. Given a set of locations where a species has been observed, the goal is to build a model to predict…