Optimal search for a randomly moving object in a special case

Abstract

Search for an object whose motion is a symmetrical two-dimensional diffusion process is considered in the case where a given amount of search of constant density is distributed, during a given interval of time, over a fixed circular area. An expression for the probability of detection of the object during this interval of time is derived in the special case where the location of the object at time zero is given. The application of this expression would involve numerical work.