Generalised linear search plan for a \(d\)-dimensional random walk target (Q2205085)

Summary: In this paper, we present a mathematical search model that studies the generalised linear search plan for detecting a \(d\)-dimensional random walk target. The target will meet one of the searchers where each searcher starts its motion from any point rather than the origin on \(n\)-disjoint real lines in \(\mathbb{R}^{n}\). Rather than, finding the conditions that show the finiteness of this search plan, we study the existence of the optimal search plan that minimises the expected value of the first meeting time between one of the searchers and the target.