Improved Hölder continuity near the boundary of one-dimensional super-Brownian motion

On the absolute continuity of one-dimensional SDE’s driven by a fractional Brownian motion

The problem of absolute continuity for a class of SDE’s driven by a real fractional Brownian motion of any Hurst index is adressed. First, we give an elementary proof of the fact that the solution to the SDE has a positive density for all t > 0 when the diffusion coefficient does not vanish, echoing in the fractional Brownian framework the main result we had previously obtained for Marcus equat...

Large Deviations for the Three Dimensional Super-brownian Motion

Let t (dx) denote a three dimensional super-Brownian motion with deterministic initial state 0 (dx) = dx, the Lebesgue measure. Let V : R 3 7 ! R be HH older continuous with compact support, not identically zero and such that Z R 3 V (x)dx = 0. We show that log P Z t 0 Z R 3 V (x) s (dx)ds > bt 3=4 is of order t 1=2 as t ! 1, for b > 0. This should be compared with the known result for the case...

Super-Brownian Motion with Extra Birth at One Point

A super-Brownian motion in two and three dimensions is constructed where “particles” give birth at a higher rate, if they approach the origin. Via a log-Laplace approach, the construction is based on Albeverio et al. (1995) who calculated the fundamental solutions of the heat equation with one-point potential in dimensions less than four.

The span of one-dimensional multiparticle Brownian motion

The number of distinct sites visited by a random walker is considered one of the basic properties in lattice random walks. In one-dimension, the ‘‘number of sites’’ is equivalent to the ‘‘span’’ of a diffusion process namely, to the furthest point from the origin visited by time t . In the continuous limit, the average span is closely related to the first moment in extrema statistics. In recent...

The average density of super-Brownian motion