Occupation times of branching systems with initial inhomogeneous Poisson states and related superprocesses.
On a Class of Discrete Distributions Arising from the Birth-Death-with-Immigration Process.
On a functional equation with asymptotically unique continuous solutions. (Short Communication).
On a functional equation with asymptotically unique continuous solutions.
On a Schröder equation arising in branching processes.
On absorption times and Dirichlet eigenvalues
This paper gives a stochastic representation in spectral terms for the absorption time T of a finite Markov chain which is irreducible and reversible outside the absorbing point. This yields quantitative informations on the parameters of a similar representation due to O'Cinneide for general chains admitting real eigenvalues. In the discrete time setting, if the underlying Dirichlet eigenvalues (namely the eigenvalues of the Markov transition operator restricted to the functions vanishing on...
On convergence of population processes in random environments to the stochastic heat equation with colored noise.
On Feller's branching diffusion processes
On long time almost sure asymptotics of renormalized branching diffusion processes
On moments for branching processes
On the 2-orthogonal polynomials and the generalized birth and death processes.
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