Related papers: Sample paths of continuous-state branching process…
We consider a critical branching process in an i.i.d. random environment, in which one immigrant arrives at each generation. We are interested in the event $\mathcal{A}_i(n)$ that all individuals alive at time $n$ are offspring of the…
In this paper we consider the unique nonnegative solution to the following generalized version of the stochastic differential equation for a continuous-state branching process. \beqnn X_t \ar=\ar x+\int_0^t\gamma_0(X_s)\dd…
We are interested in the dynamic of a structured branching population where the trait of each individual moves according to a Markov process. The rate of division of each individual is a function of its trait and when a branching event…
How high should be the rate of immigration into a stochastic population in order to significantly reduce the probability of observing the population extinct? Is there any relation between the population size distributions with and without…
We study a class of interacting particle systems on $\mathbb{R}$ with two types. Particles evolve by independent jumps sampled from a fixed distribution, with type-dependent jump rates $v_+$, $v_-$ and stochastic type switching driven by…
We analyze the stationary tail of a fixed-point equation arising in branching processes with state-independent immigration, when both immigration and offspring distributions have heavy tails with boundary index one. We prove that \[ P(X >…
A non-critical branching immigration superprocess with dependent spatial motion is constructed and characterized as the solution of a stochastic equation driven by a time-space white noise and an orthogonal martingale measure. A…
Stationary stochastic processes with independent increments, of which the Poisson process is a prominent example, are widely used to describe real world events. With the basic assumption that a counting process is stationary and has…
In this paper we consider a triangular array of branching processes with non-stationary immigration. We prove a weak convergence of properly normalized branching processes with immigration to deterministic function under assumption that…
These notes were used in a short graduate course on branching processes the author gave in Beijing Normal University. The following main topics are covered: scaling limits of Galton--Watson processes, continuous-state branching processes,…
In this article we provide a sufficient condition for a continuous-state branching process with immigration (CBI process) to not hit its boundary, i.e. for non-extinction. Our result applies to arbitrary dimension $d \geq 1$ and is…
In this paper, we firstly give a reconstruction for Crump-Mode-Jagers processes with immigration as solutions to a class of stochastic Volterra integral equations, which offers us a new insight for the evolution dynamics of age-dependent…
We consider a system of independent one-dimensional random walkers where new particles are added at the origin at fixed rate whenever there is no older particle present at the origin. A Poisson ansatz leads to a semi-linear lattice heat…
In this work we model the dynamics of a population that evolves as a continuous time branching process with a trait structure and ecological interactions in form of mutations and competition between individuals. We generalize existing…
In this paper, a special sequence of controlled branching processes is considered. We provide a simple set of sufficient conditions for the weak convergence of such processes to a weak solution to a kind of continuous branching processes…
Multitype branching processes with immigration in one type are used to model the dynamics of stage-structured plant populations. Parametric inference is first carried out when count data of all types are observed. Statistical…
We investigate a piecewise-deterministic Markov process, evolving on a Polish metric space, whose deterministic behaviour between random jumps is governed by some semi-flow, and any state right after the jump is attained by a randomly…
In this work we study the long-time behavior for subcritical measure-valued branching processes with immigration on the space of tempered measures. Under some reasonable assumptions on the spatial motion, the branching and immigration…
A two-type continuous-state branching process in varying environments is constructed as the pathwise unique solution of a system of stochastic equations driven by time-space noises, where the pathwise uniqueness is derived from a comparison…
We give sufficient conditions on the initial, offspring and immigration distributions under which the distribution of a not necessarily stationary Galton--Watson process with immigration is regularly varying at any fixed time.