Deterministic Pursuit of Randomly Moving Targets

In this chapter, we explore several mathematical models describing the pursuit of an object moving randomly in a one- or two-dimensional space. Our central focus lies in analytically calculating the mean capture time within these models, treating it as a mean first passage time. In certain special cases, we can derive exact expressions, which we subsequently utilize to develop approximations valid for the general scenarios. We examine how this statistical measure is influenced by both the diffusion coefficient of the target and the number of chasers involved. Additionally, we explore strategies for optimizing the pursuit from the hunters’ perspective. Looking ahead, we consider potential generalizations and extensions of the model.