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We study a branching random walk on $ℝ$ 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.

J.B. Walsh, R.T. Smythe (1973)

Inventiones mathematicae

The Fermat cubic, elliptic functions, continued fractions, and a combinatorial excursion.

Van Fossen Conrad, Eric, Flajolet, Philippe (2005)

Séminaire Lotharingien de Combinatoire [electronic only]

The Kolmogorov equation in the stochastic fragmentation theory and branching processes with infinite collection of particle types.

Brodskii, R.Ye., Virchenko, Yu.P. (2006)

Abstract and Applied Analysis

The Martin entrance boundary of the Galton–Watson process

Gerold Alsmeyer, Uwe Rösler (2006)

Annales de l'I.H.P. Probabilités et statistiques

The modification of the Galton-Watson process.

Kalas, J. (1996)

Acta Mathematica Universitatis Comenianae. New Series

The multifractal structure of super-brownian motion

Edwin A. Perkins, S. James Taylor (1998)

Annales de l'I.H.P. Probabilités et statistiques

The number of absorbed individuals in branching brownian motion with a barrier

Pascal Maillard (2013)

Annales de l'I.H.P. Probabilités et statistiques

We study supercritical branching Brownian motion on the real line starting at the origin and with constant drift $c$ . At the point $x g t; 0$ , 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 $c_{0}$ , such that this process becomes extinct almost surely if and only if $c \geq c_{0}$ . In this case, if $Z_{x}$ denotes the number of individuals absorbed at the barrier, we give an asymptotic for $P (Z_{x} = n)$ as $n$ goes to infinity. If $c = c_{0}$ ...

The two uniform infinite quadrangulations of the plane have the same law

Laurent Ménard (2010)

Annales de l'I.H.P. Probabilités et statistiques

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

Simon C. Harris, Matthew I. Roberts (2012)

Annales de l'I.H.P. Probabilités et statistiques

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...

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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

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

The two uniform infinite quadrangulations of the plane have the same law

The unscaled paths of branching brownian motion

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.

Transient analysis of a queue where potential customers are discouraged by queue length.

Transient probabilities for a simple birth-death-immigration process under the influence of total catastrophes.

Currently displaying 1 – 20 of 23