David Brillinger - Some aspects of the motion of particles described by stochastic differential equations

Consider a particle moving on the surface of the unit sphere in R³and heading towards a specific destination with a constant average speed, but subject to random deviations. The motion is modelled as a diffusion with drift restricted to the surface of the sphere. Expressions are set down for various characteristics of the process including expected travel time to a cap, the limiting distribution, the likelihood ratio and some estimates for parameters appearing in the model.

The cases of motion near the surface of the sphere and where explanatory variables are present are also considered.