Multidimensional random motions with a natural number of finite velocities

We present a detailed analysis of random motions moving in higher spaces with a natural number of velocities. In the case of the so-called minimal random dynamics, under some broad assumptions, we give the joint distribution of the position of the motion (for both the inner part and the boundary of...

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Bibliographic Details
Published in:Advances in applied probability 2024-09, Vol.56 (3), p.1033-1063
Main Authors: Cinque, Fabrizio, Cintoli, Mattia
Format: Article
Language:English
Subjects:
Mathematical problems
Original Article
Partial differential equations
Probability
Random variables
Stochastic models
Velocity
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Summary:We present a detailed analysis of random motions moving in higher spaces with a natural number of velocities. In the case of the so-called minimal random dynamics, under some broad assumptions, we give the joint distribution of the position of the motion (for both the inner part and the boundary of the support) and the number of displacements performed with each velocity. Explicit results for cyclic and complete motions are derived. We establish useful relationships between motions moving in different spaces, and we derive the form of the distribution of the movements in arbitrary dimension. Finally, we investigate further properties for stochastic motions governed by non-homogeneous Poisson processes.
ISSN:0001-8678
1475-6064
DOI:10.1017/apr.2024.26