99,449 research outputs found
A family of random walks with generalized Dirichlet steps
We analyze a class of continuous time random walks in
with uniformly distributed directions. The steps performed by these processes
are distributed according to a generalized Dirichlet law. Given the number of
changes of orientation, we provide the analytic form of the probability density
function of the position reached, at time
, by the random motion. In particular, we analyze the case of random walks
with two steps.
In general, it is an hard task to obtain the explicit probability
distributions for the process . Nevertheless,
for suitable values for the basic parameters of the generalized Dirichlet
probability distribution, we are able to derive the explicit conditional
density functions of . Furthermore, in some
cases, by exploiting the fractional Poisson process, the unconditional
probability distributions are obtained. This paper extends in a more general
setting, the random walks with Dirichlet displacements introduced in some
previous papers
Random walks and branching processes in correlated Gaussian environment
We study persistence probabilities for random walks in correlated Gaussian
random environment first studied by Oshanin, Rosso and Schehr. From the
persistence results, we can deduce properties of critical branching processes
with offspring sizes geometrically distributed with correlated random
parameters. More precisely, we obtain estimates on the tail distribution of its
total population size, of its maximum population, and of its extinction time
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