Abstract
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.
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Brillinger, D.R. A Particle Migrating Randomly on a Sphere. Journal of Theoretical Probability 10, 429–443 (1997). https://doi.org/10.1023/A:1022869817770
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DOI: https://doi.org/10.1023/A:1022869817770