Random Motions at Finite Velocity on Non-Euclidean Spaces

Francesco Cybo Ottone and Enzo Orsingher ()
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Francesco Cybo Ottone: Independent Researcher, 00152 Rome, Italy
Enzo Orsingher: Dipartimento di Scienze Statistiche, Sapienza Università di Roma, 00185 Rome, Italy

Mathematics, 2022, vol. 10, issue 23, 1-12

Abstract: 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 ( P 0 , P t ) from the starting point P 0 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.

Keywords: hyperbolic geometry; spherical geometry; Carnot hyperbolic and spherical formulas; finite velocity motions (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
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