Related papers: Total progeny for spectrally negative branching L{…
Small-space and large-time estimates and asymptotic expansion of the distribution function and (the derivatives of) the density function of hitting times of points for symmetric L\'evy processes are studied. The L\'evy measure is assumed to…
We apply the spectral method, recently developed by the authors, to calculate the statistics of a reaction-limited multi-step birth-death process, or chemical reaction, that includes as elementary steps branching A->2A and annihilation…
We consider a continuous-time branching random walk on $\mathbb{Z}$ in a random non homogeneous environment. Particles can walk on the lattice points or disappear with random intensities. The process starts with one particle at initial time…
We consider a process $Z$ on the real line composed from a L\'evy process and its exponentially tilted version killed with arbitrary rates and give an expression for the joint law of $Z$ seen from its supremum, the supremum $\overline Z$…
We study a system of particles moving on a line in the same direction. Passing is allowed and when a fast particle overtakes a slow particle, it acquires a new velocity drawn from a distribution P_0(v), while the slow particle remains…
The kinetics of the annihilation process, $A+A\to 0$, with ballistic particle motion is investigated when the distribution of particle velocities is {\it discrete}. This discreteness is the source of many intriguing phenomena. In the mean…
Extinction transition of bacteria under forced rotation is analyzed in pie geometry. Under convection, separation of the radial and the azimuthal degrees of freedom is not possible, and the linearized evolution operator is diagonalized…
A branching process in varying environment with generation-dependent immigration is a modification of the standard branching process in which immigration is allowed and the reproduction and immigration laws may vary over the generations.…
For a spectrally negative L\'evy process (snLp) $X$, killed according to a rate that is a function $\omega$ of its position, we analyse the exit probability of the one-sided upwards-passage problem. When $\omega$ is strictly positive, this…
We investigate the long-time evolution of branching diffusion processes (starting with a finite number of particles) in inhomogeneous media. The qualitative behavior of the processes depends on the intensity of the branching. In the…
We consider the critical branching processes in correlated random environment which is positively associated and study the probability of survival up to the n-th generation. Moreover, when the environment is given by fractional Brownian…
We give conditions under which the tail probability of the supremum over unit interval of a Levy process with light tail is equivalent to the tail of the value of the process at the right endpoint.
It is well known that under some conditions the almost sure survival probability of a multitype branching processes in random environment is positive if the Lyapunov exponent corresponding to the expectation matrices is positive, and zero…
We study the spread of an infection on top of a moving population. The environment evolves as a zero range process on the integer lattice starting in equilibrium. At time zero, the set of infected particles is composed by those which are on…
We consider a system of particles performing a one-dimensional dyadic branching Brownian motion with space-dependent branching rate, negative drift $-\mu$ and killed upon reaching $0$, starting with $N$ particles. More precisely, particles…
In phylogenetic studies, the evolution of molecular sequences is assumed to have taken place along the phylogeny traced by the ancestors of extant species. In the presence of lateral gene transfer (LGT), however, this may not be the case,…
This paper studies systems of particles following independent random walks and subject to annihilation, binary branching, coalescence, and deaths. In the case without annihilation, such systems have been studied in our 2005 paper…
A multitype continuous-state branching process (MCSBP) ${\rm Z}=({\rm Z}_{t})_{t\geq 0}$, is a Markov process with values in $[0,\infty)^{d}$ that satisfies the branching property. Its distribution is characterised by its branching…
This article studies the quasi-stationary behaviour of population processes with unbounded absorption rate, including one-dimensional birth and death processes with catastrophes and multi-dimensional birth and death processes, modeling…
We consider a L\'evy process reflected at the origin with additional i.i.d. collapses that occur at Poisson epochs, where a collapse is a jump downward to a state which is a random fraction of the state just before the jump. We first study…