Existence of a finite multiplicative search plan with random distances and velocities to find a d-dimensional Brownian target

Abstract

We present the existence of a finite search plan to find Brownian target on the d-space by using d-searchers. Each searcher moves continuously in both directions of the origin (starting point) of the line (field of its search) with random distances and velocities. We express theses distances and velocities with independent random variables with known probability density functions (PDFs). We present more analysis about the density of the random distances in our model by using Fourier–Laplace representation. This analysis will provide us with the conditions that make the expected value of the first meeting time between the target and one of the searchers finite.

Keywords

• random search
• brownian motion
• fourier–laplace representation