[Author]
Vladislav Vysotsky
[Title]
A functional limit theorem for the position of a particle
in a Lorentz type model
[AMS Subj-class]
60K37 Processes in random environments
[Abstract]
Consider a particle moving through a random medium, which consists
of spherical obstacles, randomly distributed in $\R^3$.
The particle is accelerated by a constant external field; when
colliding with an obstacle, the particle inelastically reflects.
We study the asymptotics of $X(t)$, which denotes the position of
the particle at time $t$, as $t \to \infty$. The result is a
functional limit theorem for $X(t)$.
[Keywords]
Lorentz model, motion in random medium, functional central limit theorem
for Markov chains, limit theorems
[Comments]
LaTeX, English, 19 pp.
The paper is accepted to "Markov Processes and Related Fields".
[Contact e-mail]
vysotsky@vv9034.spb.edu