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Stochastic motions on the 3-sphere governed by wave and heat equations

Published online by Cambridge University Press:  14 July 2016

Enzo Orsingher
Enzo Orsingher*
Affiliation:
University of Rome
*
∗Postal address: Dipartimento di Statistica, Probabilità e Statistiche Applicate, Facoltà di Statistica, Università degli Studi di Roma ‘La Sapienza', Piazzale Aldo Moro 5, 00185 Roma, Italy.
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Abstract

In this paper a random motion on the surface of the 3-sphere whose probability law is a solution of the telegraph equation in spherical coordinates is presented. The connection of equations governing the random motion with Maxwell equations is examined together with some qualitative features of its sample paths. Finally Brownian motion on the 3-sphere is derived as the limiting process of a random walk with latitude-changing probabilities.

Keywords

RANDOM WALKSTELEGRAPH EQUATIONPOISSON PROCESSMAXWELL EQUATIONSBROWNIAN MOTION
Type
Research Papers
Information
Journal of Applied Probability , Volume 24 , Issue 2 , June 1987 , pp. 315 - 327
Copyright
Copyright © Applied Probability Trust 1987 

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References

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