We prove that the law of the euclidean norm of an n-dimensional Brownian bridge is, in general, only equivalent and not equal to the law of a n-dimensional Bessel bridge and we compute explicitly the mutual density. Relations with Bessel processes with drifts are also discussed.

In this note we consider a branching Brownian motion (BBM) on in which a particle at spatial position y splits into two at rate [beta]y2, where [beta]0 is a constant. This is a critical breeding rate for BBM in the sense that the expected population size blows up in finite time while the...

We develop an idea of Evans and O'Connell (1994) [13], Engländer and Pinsky (1999) [10] and Duquesne and Winkel (2007) [4] by giving a pathwise construction of the so-called 'backbone' decomposition for supercritical superprocesses. Our results also complement a related result for critical...