Searching for a d-dimensional Brownian target with multiple sensors

We consider a search problem for a d-dimensional Brownian target that moves randomly on d-space. We have n-searchers moving with a linear paths in d-dimension to search for the target. Each of the searchers moves continuously along its line in both directions of the starting point (origin of its line). The purpose of this paper is to formulate a search model and find the condition under which the expected value of the first meeting time between one of the searchers and the target finite. Also, we show the existence of the optimal search plan that minimises the expected value of the first meeting time.