972 research outputs found
On the local time of random walks associated with Gegenbauer polynomials
The local time of random walks associated with Gegenbauer polynomials
is studied in the recurrent case: $\alpha\in\
[-\frac{1}{2},0]\alpha\bbN$.Comment: 12 page
Persistence exponent for discrete-time, time-reversible processes
We study the persistence probability for some discrete-time, time-reversible
processes. In particular, we deduce the persistence exponent in a number of
examples: first, we deal with random walks in random sceneries (RWRS) in any
dimension with Gaussian scenery. Second, we deal with sums of stationary
Gaussian sequences with correlations exhibiting long-range dependence. Apart
from the persistence probability we deal with the position of the maximum and
the time spent on the positive half-axis by the process
Persistence exponent for random walk on directed versions of
We study the persistence exponent for random walks in random sceneries (RWRS)
with integer values and for some special random walks in random environment in
including random walks in with random orientations
of the horizontal layers.Comment: 19 page
Renewal theorems for random walks in random scenery
Random walks in random scenery are processes defined by
, where and
are two independent sequences of i.i.d. random
variables. We suppose that the distributions of and belong to the
normal domain of attraction of strictly stable distributions with index
and respectively. We are interested in the
asymptotic behaviour as goes to infinity of quantities of the form
(when is transient) or
(when is recurrent) where
is some complex-valued function defined on or
A functional approach for random walks in random sceneries
A functional approach for the study of the random walks in random sceneries
(RWRS) is proposed. Under fairly general assumptions on the random walk and on
the random scenery, functional limit theorems are proved. The method allows to
study separately the convergence of the walk and of the scenery: on the one
hand, a general criterion for the convergence of the local time of the walk is
provided, on the other hand, the convergence of the random measures associated
with the scenery is studied. This functional approach is robust enough to
recover many of the known results on RWRS as well as new ones, including the
case of many walkers evolving in the same scenery.Comment: 23
Random walks on FKG-horizontally oriented lattices
We study the asymptotic behavior of the simple random walk on oriented
version of . The considered latticesare not directed on the
vertical axis but unidirectional on the horizontal one, with symmetric random
orientations which are positively correlated. We prove that the simple random
walk is transient and also prove a functionnal limit theorem in the space of
cadlag functions, with an unconventional normalization.Comment: 16 page
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