Sur un processus de vie et de mort de particules sur [0,1]
Survival probabilities for branching Brownian motion with absorption.
The analytic fixed point function. II.
The asymptotic composition of supercritical, multi-type branching populations
The branching process in a brownian excursion
The center of mass of the ISE and the Wiener index of trees.
The compact support property for measure-valued processes
The critical barrier for the survival of branching random walk with absorption
We study a branching random walk on with an absorbing barrier. The position of the barrier depends on the generation. In each generation, only the individuals born below the barrier survive and reproduce. Given a reproduction law, Biggins et al. [Ann. Appl. Probab.1(1991) 573–581] determined whether a linear barrier allows the process to survive. In this paper, we refine their result: in the boundary case in which the speed of the barrier matches the speed of the minimal position of a particle...
The Existence of Dual Processes.
The Fermat cubic, elliptic functions, continued fractions, and a combinatorial excursion.
The Kolmogorov equation in the stochastic fragmentation theory and branching processes with infinite collection of particle types.
The Martin entrance boundary of the Galton–Watson process
The modification of the Galton-Watson process.
The multifractal structure of super-brownian motion
The number of absorbed individuals in branching brownian motion with a barrier
We study supercritical branching Brownian motion on the real line starting at the origin and with constant drift . At the point , we add an absorbing barrier, i.e. individuals touching the barrier are instantly killed without producing offspring. It is known that there is a critical drift , such that this process becomes extinct almost surely if and only if . In this case, if denotes the number of individuals absorbed at the barrier, we give an asymptotic for as goes to infinity. If ...
The two uniform infinite quadrangulations of the plane have the same law
We prove that the uniform infinite random quadrangulations defined respectively by Chassaing–Durhuus and Krikun have the same distribution.
The unscaled paths of branching brownian motion
For a set A ⊂ C[0, ∞), we give new results on the growth of the number of particles in a branching Brownian motion whose paths fall within A. We show that it is possible to work without rescaling the paths. We give large deviations probabilities as well as a more sophisticated proof of a result on growth in the number of particles along certain sets of paths. Our results reveal that the number of particles can oscillate dramatically. We also obtain new results on the number of particles near the...
The width of Galton-Watson trees conditioned by the size.
Théorèmes ergodiques pour un processus de naissance et mort sur la droite réelle
Transient analysis in discrete time of Markovian queues with quadratic rates.