A particle migrating randomly on a sphere. (English) Zbl 0892.60084
Summary: Consider a particle moving on the surface of the unit sphere in \(R^3\) and heading towards a specific destination with a constant average speed, but subject to random deviations. The motion is modeled 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.
MSC:
| 60J60 | Diffusion processes |
| 60J80 | Branching processes (Galton-Watson, birth-and-death, etc.) |
| 60J65 | Brownian motion |
| 60H10 | Stochastic ordinary differential equations (aspects of stochastic analysis) |
