Random walk models for search with particular reference to a bounded region
The position of a target moving randomly in an area is described. The motion is a sequence of finite legs traversed at constant speed, with exponentially distributed lengths, and randomly oriented directions with respect to each other. Following \textit{J. C. Kluyver} [A local probability problem. Proc. Sect. Sci., Koninkl. Akad. Wetensch. Amsterdam 8, 341-350 (1906)] a new expression is derived for the distribution of the radius vector where the walk is of ''Pearson'' type, the relative directions of successive legs being U(0,2\(\pi)\). This is followed by a study of such a walk within a circular area. The purpose here is to investigate the effect of reflection policies at the boundary on the distribution of the position of the target within the area and on the coverage of the area by the walk.
scientific article; zbMATH DE number 4005312