相关论文: Local extinction in continuous-state branching pro…
Analytical solutions for time-inhomogeneous linear birth-death processes with immigration are derived. While time-inhomogeneous linear birth-death processes without immigration have been studied by using a generating function approach, the…
Scaling limits for continuous-time branching processes with discrete state space are provided as the initial state tends to infinity. Depending on the finiteness or non-finiteness of the mean and/or the variance of the offspring…
We consider a null-recurrent randomly biased walk $\mathbb{X}$ on a Galton-Watson tree in the (sub)-diffusive regime and we prove that properly renormalized, the local time in a critical generation converges in law towards some function of…
A continuous-state branching process in varying environments is constructed by the pathwise unique solution to a stochastic integral equation driven by time-space noises. The process arises naturally in the limit theorem of Galton--Watson…
A curious connection exists between the theory of optimal stopping for independent random variables, and branching processes. In particular, for the branching process $Z_n$ with offspring distribution $Y$, there exists a random variable $X$…
We develop a new methodology for the fluctuation theory of continuous-time skip-free Markov chains, extending the recent work of Choi and Patie [5] for discrete-time skip-free Markov chains. As the main application we use it to derive a…
We consider a population growth model given by a two-type continuous-state branching process with immigration and competition, introduced by Ma. We study the relative frequency of one of the types in the population when the total mass is…
Limit behaviour of temporal and contemporaneous aggregations of independent copies of a stationary multitype Galton-Watson branching process with immigration is studied in the so-called iterated and simultaneous cases, respectively. In both…
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…
We consider a branching-selection particle system on the real line. In this model the total size of the population at time $n$ is limited by $\exp\left(a n^{1/3}\right)$. At each step $n$, every individual dies while reproducing…
We obtain local weak limits in probability for Collapsed Branching Processes (CBP), which are directed random networks obtained by collapsing random-sized families of individuals in a general continuous-time branching process. The local…
In this somewhat didactic note we give a detailed alternative proof of the known result due to Wei and Winnicki (1989) which states that under second order moment assumptions on the offspring and immigration distributions the sequence of…
We construct a stationary Markov process corresponding to the evolution of masses and distances of subtrees along the spine from the root to a branch point in a conjectured stationary, continuum random tree-valued diffusion that was…
We revisit certain decompositions of continuous-state branching processes (CSBPs), commonly referred to as skeletal decompositions, through the lens of intertwining of semi-groups. Precisely, we associate to a CSBP $X$ with branching…
A controlled branching process (CBP) is a modification of the standard Bienaym\'e-Galton-Watson process in which the number of progenitors in each generation is determined by a random mechanism. We consider a CBP starting from a random…
We study by duality methods the extinction and explosion times of continuous-state branching processes with logistic competition (LCSBPs) and identify the local time at $\infty$ of the process when it is instantaneously reflected at…
Continuous-time branching processes (CTBPs) are powerful tools in random graph theory, but are not appropriate to describe real-world networks, since they produce trees rather than (multi)graphs. In this paper we analyze collapsed branching…
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…
Let $\{Z_n^i = (Z_n^i(r))_{1 \le r \le d}: n \ge 0\}$ be a supercritical $d$-type branching process in an i.i.d. environment $\xi = (\xi_0, \xi_1, \dots)$, starting from a single particle of type $i$. The offspring distribution at…
Consider a continuous-state branching population constructed as a flow of nested subordinators. Inverting the subordinators and reversing time give rise to a flow of coalescing Markov processes (with negative jumps) which correspond to the…