An existential study of a tracking model for a two-dimensional Brownian particle on a planar surface

Abstract

This paper discusses the existence of the tracking technique for a two-dimensional Brownian particle on a planar surface. The tracking process starts from the origin of the plane (intersection point of [Formula: see text] and [Formula: see text] axes). Accordingly, we derive the conditions that make the expected value of the first meeting time between the sensor and the particle finite. Also, we calculate the approximated expected value of the first meeting time.