Series representations for the characteristic function of the multidimensional Markov random flight

TL;DR

This paper introduces two series representations for the characteristic function of multidimensional symmetric Markov random flights, utilizing Bessel functions and time variables, along with an asymptotic formula for a mixed moment function.

Contribution

It provides novel series representations of the characteristic function for multidimensional Markov random flights and an asymptotic formula for a specific mixed moment function.

Findings

Series representations using Bessel functions and time variables.

Asymptotic formula for the second mixed moment in 3D.

Enhanced understanding of the probabilistic structure of Markov random flights.

Abstract

Two series representations of the characteristic function of the multidimensional symmetric Markov random flight with respect to Bessel functions and with respect to time variable, are given. Asymptotic formula for the second mixed moment function of the three-dimensional random flight is presented.