On the behavior of LIFO preemptive resume queues in heavy traffic.
On the birth-and-assassination process, with an application to scotching a rumor in a network.
On the central limit theorem for some birth and death processes
Suppose that {Xn, n ≥ 0} is a stationary Markov chain and V is a certain function on a phase space of the chain, called an observable. We say that the observable satisfies the central limit theorem (CLT) if [...] [...] converge in law to a normal random variable, as N → +∞. For a stationary Markov chain with the L2 spectral gap the theorem holds for all V such that V (X0) is centered and square integrable, see Gordin [7]. The purpose of this article is to characterize a family of observables V for...
On the distribution of the number of vertices in layers of random trees.
On the equivalence of addition formula of lattice paths and the Kolmogorov equation of birth and death processes.
On the Extinction Probability for Bisexual Branching Processes in Varying Environments
2000 Mathematics Subject Classification: 60J80In this paper, the bisexual branching process in varying environments introduced in [9] is considered and some sufficient conditions for the existence of positive probability of non-extinction are established.Research supported by the Plan Nacional de Investigación Científica, Desarrollo e Innovación Tecnológica, grant BFM2000-0356 and the Consejería de Educación, Ciencia y Tecnología de la Junta de Extremadura and the Fondo Social Europeo, grant IPR00A056....
On the Integrability of the Limit of a Supercritical Branching Process
On the left tail asymptotics for the limit law of supercritical Galton–Watson processes in the Böttcher case
Under a well-known scaling, supercritical Galton–Watson processes Z converge to a non-degenerate non-negative random limit variable W. We are dealing with the left tail (i.e. close to the origin) asymptotics of its law. In the Böttcher case (i.e. if always at least two offspring are born), we describe the precise asymptotics exposing oscillations (Theorem 1). Under a reasonable additional assumption, the oscillations disappear (Corollary 2). Also in the Böttcher case, we improve a recent lower deviation...
On the martingale problem for super-brownian motion
On the Maximum of a Branching Process Conditioned on the Total Progeny
The maximum M of a critical Bienaymé-Galton-Watson process conditioned on the total progeny N is studied. Imbedding of the process in a random walk is used. A limit theorem for the distribution of M as N → ∞ is proved. The result is trasferred to the non-critical processes. A corollary for the maximal strata of a random rooted labeled tree is obtained.
On the occupation measure of super-Brownian motion.
On the re-rooting invariance property of Lev́y trees.
On the Structure of Spatial Branching Processes
The paper is a contribution to the theory of branching processes with discrete time and a general phase space in the sense of [2]. We characterize the class of regular, i.e. in a sense sufficiently random, branching processes (Φk) k∈Z by almost sure properties of their realizations without making any assumptions about stationarity or existence of moments. This enables us to classify the clans of (Φk) into the regular part and the completely non-regular part. It turns out that the completely non-regular branching...
On the Survival Probability of a Branching Process in a Random Environment
On the survival probability of a branching process in a random environment
Parking functions, empirical processes, and the width of rooted labeled trees.
Perturbing transient random walk in a random environment with cookies of maximal strength
We consider a left-transient random walk in a random environment on that will be disturbed by cookies inducing a drift to the right of strength 1. The number of cookies per site is i.i.d. and independent of the environment. Criteria for recurrence and transience of the random walk are obtained. For this purpose we use subcritical branching processes in random environments with immigration and formulate criteria for recurrence and transience for these processes.
Poisson point process limits in size-biased Galton-Watson trees.
Population-size-dependent branching processes.
Positively and negatively excited random walks on integers, with branching processes.