A Particle Migrating Randomly on a Sphere

• Main Author: David R. Brillinger
• Other Authors: The Pennsylvania State University CiteSeerX Archives
• Format: Text
• Language: English
• Published: 1997
• Subjects: KEY WORDS; Drift; Great circle path; Likelihood ratio; Pole-seeking; Skew product; Spherical Brownian motion; Stochastic differential equation; Travel time; Elephant Seals
• Online Access: http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.52.4717; http://www.stat.berkeley.edu/~brill/Papers/rosenblatt.ps

INTRODUCTION There are marine mammals, such as elephant seals, that travel great distances and are tracked. It is of interest to biologists to describe the routes. One can wonder for example if the animals follow great circle paths. The animals will be foraging along the way, i.e. pulled away from the direct route from origin to destination, and this may be modelled as stochastic fluctuations. The great circle route is the geodesic, providing the shortest trip. A ship needs to be changing course continually to stay ____________ 1 Statistics Department, University of California, Berkeley, CA 94720-3860, USA - 2 - on it. It is intriguing that some animals apparently do not need to change course, they can keep going straight ahead. An issue that arises in modelling the physical world is whether to work employing the Ito or the Stratonovich calculus. Reasons have been presented various places to the effect that when developing physical a