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Multidimensional random motions with a natural number of finite velocities

Part of: Special processes Stochastic processes

Published online by Cambridge University Press:  22 March 2024

Fabrizio Cinque Open the ORCID record for Fabrizio Cinque [Opens in a new window]  and
Mattia Cintoli
Fabrizio Cinque*
Affiliation:
Sapienza University of Rome
Mattia Cintoli*
Affiliation:
Sapienza University of Rome
*
*Postal address: Department of Statistical Sciences, Sapienza University of Rome, Italy.
*Postal address: Department of Statistical Sciences, Sapienza University of Rome, Italy.
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Abstract

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.

Keywords

Motions in higher spacetelegraph processconvexitypartial differential equationsnon-homogeneous Poisson process

MSC classification

Primary: 60K99: None of the above, but in this section
Secondary: 60G50: Sums of independent random variables; random walks
Type
Original Article
Information
Advances in Applied Probability , First View , pp. 1 - 31
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Copyright
© The Author(s), 2024. Published by Cambridge University Press on behalf of Applied Probability Trust

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