Random Motions at Finite Velocity on Non-Euclidean Spaces

In this paper, random motions at finite velocity on the Poincaré half-plane and on the unit-radius sphere are studied. The moving particle at each Poisson event chooses a uniformly distributed direction independent of the previous evolution. This implies that the current distance d(P0,Pt) from the s...

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Veröffentlicht in:Mathematics (Basel) 2022-12, Vol.10 (23), p.4609
Hauptverfasser: Cybo Ottone, Francesco, Orsingher, Enzo
Format: Artikel
Sprache:eng
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Zusammenfassung:In this paper, random motions at finite velocity on the Poincaré half-plane and on the unit-radius sphere are studied. The moving particle at each Poisson event chooses a uniformly distributed direction independent of the previous evolution. This implies that the current distance d(P0,Pt) from the starting point P0 is obtained by applying the hyperbolic Carnot formula in the Poincaré half-plane and the spherical Carnot formula in the analysis of the motion on the sphere. We obtain explicit results of the conditional and unconditional mean distance in both cases. Some results for higher-order moments are also presented for a small number of changes of direction.
ISSN:2227-7390
2227-7390
DOI:10.3390/math10234609