7,926 research outputs found
Moderate deviations for diffusions with Brownian potentials
We present precise moderate deviation probabilities, in both quenched and
annealed settings, for a recurrent diffusion process with a Brownian potential.
Our method relies on fine tools in stochastic calculus, including Kotani's
lemma and Lamperti's representation for exponential functionals. In particular,
our result for quenched moderate deviations is in agreement with a recent
theorem of Comets and Popov [Probab. Theory Related Fields 126 (2003) 571-609]
who studied the corresponding problem for Sinai's random walk in random
environment.Comment: Published at http://dx.doi.org/10.1214/009117904000000829 in the
Annals of Probability (http://www.imstat.org/aop/) by the Institute of
Mathematical Statistics (http://www.imstat.org
The slow regime of randomly biased walks on trees
We are interested in the randomly biased random walk on the supercritical
Galton--Watson tree. Our attention is focused on a slow regime when the biased
random walk is null recurrent, making a maximal displacement of order
of magnitude in the first steps. We study the localization
problem of and prove that the quenched law of can be approximated
by a certain invariant probability depending on and the random environment.
As a consequence, we establish that upon the survival of the system,
converges in law to some non-degenerate limit on
whose law is explicitly computed.Comment: 43 pages. We added a recent work by Jim Pitman ([38]) for the
limiting la
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