Incollection,
Transport and first passage properties of a discrete version of the Ornstein-Uhlenbeck process
Abstract Book of the XXIII IUPAP International Conference on Statistical Physics, Genova, Italy, (9-13 July 2007)
Abstract
A discrete version of the Ornstein-Uhlenbeck process, which arises as
a simple generalization of the discrete random walk, is analyzed.
The statistical properties of the free propagator for the process are
evaluated for the one dimensional case. It is shown that if the jump
distribution has finite variance the usual equation for the evolution
of the probability distribution of the Ornstein-Uhlenbeck process is
recovered in the continuum limit. However, the discrete process is
well defined also for long tailed jump distributions and can be used
to describe a Lèvy walk under the effect of a harmonic
potential. Further, some first passage properties of the process are
studied. In particular, it is shown that the universal features of
Sparre-Andersen's theorem do not extend to the discrete O-U process.
Finally, a brief discussion of the generalization of this process to
describe random walks in general potentials is presented and briefly
compared with results arising from the fractional diffusion approach.
