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Random Motions at Finite Velocity on Non-Euclidean Spaces

Author

Listed:
  • Francesco Cybo Ottone

    (Independent Researcher, 00152 Rome, Italy)

  • Enzo Orsingher

    (Dipartimento di Scienze Statistiche, Sapienza Università di Roma, 00185 Rome, Italy)

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.

Suggested Citation

  • Francesco Cybo Ottone & Enzo Orsingher, 2022. "Random Motions at Finite Velocity on Non-Euclidean Spaces," Mathematics, MDPI, vol. 10(23), pages 1-12, December.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:23:p:4609-:d:994054
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