7,813 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
A subdiffusive behaviour of recurrent random walk in random environment on a regular tree
We are interested in the random walk in random environment on an infinite
tree. Lyons and Pemantle [11] give a precise recurrence/transience criterion.
Our paper focuses on the almost sure asymptotic behaviours of a recurrent
random walk in random environment on a regular tree, which is closely
related to Mandelbrot [13]'s multiplicative cascade. We prove, under some
general assumptions upon the distribution of the environment, the existence of
a new exponent such that
behaves asymptotically like . The value of is explicitly
formulated in terms of the distribution of the environment.Comment: 29 pages with 1 figure. Its preliminary version was put in the
following web site:
http://www.math.univ-paris13.fr/prepub/pp2005/pp2005-28.htm
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