Asymptotic results for random flights

TL;DR

This paper investigates the long-term behavior of random flights, a type of stochastic process modeling biological motion, by establishing large deviation principles for both conditional and unconditional laws.

Contribution

It provides the first large deviation principles for the asymptotic behavior of random flights, enhancing understanding of their probabilistic properties.

Findings

Large deviation principles are established for conditional laws given the number of direction changes.

Large deviation principles are also proved for non-conditional laws of standard random flights.

Results contribute to the theoretical understanding of stochastic biological motion models.

Abstract

The random flights are (continuous time) random walkswith finite velocity. Often, these models describe the stochastic motions arising in biology. In this paper we study the large time asymptotic behavior of random flights. We prove the large deviation principle for conditional laws given the number of the changes of direction, and for the non-conditional laws of some standard random flights.