# Cyclic random motions in ${\mathbb{R}}^{d}$-space with n directions

ESAIM: Probability and Statistics (2006)

- Volume: 10, page 277-316
- ISSN: 1292-8100

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topLachal, Aimé. "Cyclic random motions in $\mathbb{R}^d$-space with n directions." ESAIM: Probability and Statistics 10 (2006): 277-316. <http://eudml.org/doc/249743>.

@article{Lachal2006,

abstract = {
We study the probability distribution of the location of a particle
performing a cyclic random motion in $\mathbb\{R\}^d$. The particle can take
n possible directions with different velocities and the changes of
direction occur at random times. The speed-vectors as well as the
support of the distribution form a polyhedron (the first one having
constant sides and the other expanding with time t). The
distribution of the location of the particle is made up of two
components: a singular component (corresponding to the beginning of
the travel of the particle) and an absolutely continuous component.
We completely describe the singular component and exhibit an
integral representation for the absolutely continuous one. The
distribution is obtained by using a suitable expression of the
location of the particle as well as some probability calculus
together with some linear algebra. The particular case of the
minimal cyclic motion (n=d+1) with Erlangian switching times is
also investigated and the related distribution can be expressed in
terms of hyper-Bessel functions with several arguments.
},

author = {Lachal, Aimé},

journal = {ESAIM: Probability and Statistics},

keywords = {Cyclic random motions; linear image of a
random vector; singular and absolutely continuous measures;
convexity; hyper-Bessel functions with several arguments.; linear image of a random vector; convexity; hyper-Bessel functions with several arguments},

language = {eng},

month = {9},

pages = {277-316},

publisher = {EDP Sciences},

title = {Cyclic random motions in $\mathbb\{R\}^d$-space with n directions},

url = {http://eudml.org/doc/249743},

volume = {10},

year = {2006},

}

TY - JOUR

AU - Lachal, Aimé

TI - Cyclic random motions in $\mathbb{R}^d$-space with n directions

JO - ESAIM: Probability and Statistics

DA - 2006/9//

PB - EDP Sciences

VL - 10

SP - 277

EP - 316

AB -
We study the probability distribution of the location of a particle
performing a cyclic random motion in $\mathbb{R}^d$. The particle can take
n possible directions with different velocities and the changes of
direction occur at random times. The speed-vectors as well as the
support of the distribution form a polyhedron (the first one having
constant sides and the other expanding with time t). The
distribution of the location of the particle is made up of two
components: a singular component (corresponding to the beginning of
the travel of the particle) and an absolutely continuous component.
We completely describe the singular component and exhibit an
integral representation for the absolutely continuous one. The
distribution is obtained by using a suitable expression of the
location of the particle as well as some probability calculus
together with some linear algebra. The particular case of the
minimal cyclic motion (n=d+1) with Erlangian switching times is
also investigated and the related distribution can be expressed in
terms of hyper-Bessel functions with several arguments.

LA - eng

KW - Cyclic random motions; linear image of a
random vector; singular and absolutely continuous measures;
convexity; hyper-Bessel functions with several arguments.; linear image of a random vector; convexity; hyper-Bessel functions with several arguments

UR - http://eudml.org/doc/249743

ER -

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