On the existence of the tracking model for N-dimensional Brownian particle in the fluid

Abstract

In this work, an existential study of the tracking technique of N-dimensional Brownian particle in the fluid has been discussed. A set of nano-robot sensors start the tracking process from the origin of N-dimensional space. Besides giving the conditions which present the finiteness of the expected value of the first meeting time between one of the nano-robot sensors and the particle, we provide the computational expected value of this time.