Search for a Randomly Moving Object

After a brief discussion of the operational origin of search problems, the mathematical problem is formulated. The mathematical quantity of interest is the joint density for location of the object sought and unsuccessful search. When the object moves according to a diffusion process, this joint density satisfies a parabolic equation. After the introduction of scaled variables, the search equation can be approximately solved by the “ray method”. The interpretation of the terms in the approximate solution is discussed. The case of constant diffusion and drift parameters and piecewise linear searching paths arises often in operational situations. This case is considered in detail.