A super-stable motion with infinite mean branching
A survey of the literature associated with the bisexual Galton-Watson branching process.
Almost sure finiteness for the total occupation time of an -superprocess.
Almost sure path properties of branching diffusion processes
Alpha-stable branching and beta-coalescents.
An age-dependent population equation with diffusion and delayed birth process.
An application of the voter model–super-brownian motion invariance principle
An elementary proof of Hawkes's conjecture on Galton-Watson trees.
Arbres et processus de Bellman-Harris
Arbres et processus de Galton-Watson
Asymptotic behavior of the hitting time, overshoot and undershoot for some Lévy processes
Let be a Lévy process started at , with Lévy measure . We consider the first passage time of to level , and the overshoot and the undershoot. We first prove that the Laplace transform of the random triple satisfies some kind of integral equation. Second, assuming that admits exponential moments, we show that converges in distribution as , where denotes a suitable renormalization of .
Asymptotic behavior of the hitting time, overshoot and undershoot for some Lévy processes
Let (Xt, t ≥ 0) be a Lévy process started at 0, with Lévy measure ν. We consider the first passage time Tx of (Xt, t ≥ 0) to level x > 0, and Kx := XTx - x the overshoot and Lx := x- XTx- the undershoot. We first prove that the Laplace transform of the random triple (Tx,Kx,Lx) satisfies some kind of integral equation. Second, assuming that ν admits exponential moments, we show that converges in distribution as x → ∞, where denotes a suitable renormalization of Tx.
Asymptotic equipartition properties for simple hierarchical and networked structures
We prove asymptotic equipartition properties for simple hierarchical structures (modelled as multitype Galton-Watson trees) and networked structures (modelled as randomly coloured random graphs). For example, for large n, a networked data structure consisting of n units connected by an average number of links of order n / log n can be coded by about H × n bits, where H is an explicitly defined entropy. The main technique in our proofs are large deviation principles for suitably defined empirical...
Asymptotic equipartition properties for simple hierarchical and networked structures
We prove asymptotic equipartition properties for simple hierarchical structures (modelled as multitype Galton-Watson trees) and networked structures (modelled as randomly coloured random graphs). For example, for large n, a networked data structure consisting of n units connected by an average number of links of order n / log n can be coded by about H × n bits, where H is an explicitly defined entropy. The main technique in our proofs are large deviation principles for suitably defined empirical...
Asymptotics for rooted bipartite planar maps and scaling limits of two-type spatial trees.
Asymptotics for the survival probability in a killed branching random walk
Consider a discrete-time one-dimensional supercritical branching random walk. We study the probability that there exists an infinite ray in the branching random walk that always lies above the line of slope γ − ε, where γ denotes the asymptotic speed of the right-most position in the branching random walk. Under mild general assumptions upon the distribution of the branching random walk, we prove that when ε → 0, this probability decays like exp{−(β+o(1)) / ε1/2}, where β is a positive constant...
Average properties of random walks on Galton-Watson trees
Balls left empty by a critical branching Wiener process.
Birth and death processes with absorption.
Boundedness of one-dimensional branching Markov processes.