相关论文: Computing the density of the Kesten-Stigum limit i…
We investigate Kesten-Stigum-like results for multi-type Galton-Watson processes with a countable number of types in a general setting, allowing us in particular to consider processes with an infinite total population at each generation.…
In this paper, we study a Galton-Watson process $(Z_n)$ with infinitely many types in a random ergodic environment $\bar{\xi}=(\xi_n)_{n\geq 0}$. We focus on the supercritical regime of the process, where the quenched average of the size of…
Let $(Z_n,n\geq 0)$ be a supercritical Galton-Watson process whose offspring distribution $\mu$ has mean $\lambda>1$ and is such that $\int x(\log(x))_+ d\mu(x)<+\infty$. According to the famous Kesten \& Stigum theorem, $(Z_n/\lambda^n)$…
We describe the asymptotic behavior of the conditional least squares estimator of the offspring mean for subcritical strongly stationary Galton--Watson processes with regularly varying immigration with tail index $\alpha \in (1,2)$. The…
We discuss approximations of the relative limit densities of descendants in Galton--Watson processes that follow from the Karlin--McGregor near-constancy phenomena. These approximations are based on the fast exponentially decaying Fourier…
We consider a super-critical Galton-Watson tree whose non-degenerate offspring distribution has finite mean. We consider the random trees $\tau$n distributed as $\tau$ conditioned on the n-th generation, Zn, to be of size an $\in$ N. We…
The Kesten-Stigum Theorem is a fundamental criterion for the rate of growth of a supercritical branching process, showing that an L log L condition is decisive. In critical and subcritical cases, results of Kolmogorov and later authors give…
Population genetic processes, such as the adaptation of a quantitative trait to directional selection, may occur on longer time scales than the sweep of a single advantageous mutation. To study such processes in finite populations,…
We study the evolution of the population size distribution of a critical Galton-Watson process with infinite variance of the offspring size of particles assuming that the population size is unusually small at the distant moment $n$ of…
A Galton-Watson process in varying environment is a discrete time branching process where the offspring distributions vary among generations. Based on a two-spine decomposition technique, we provide a probabilistic argument of a Yaglom-type…
We consider a particle system in continuous time, discrete population, with spatial motion and nonlocal branching. The offspring's weights and their number may depend on the mother's weight. Our setting captures, for instance, the processes…
Our principal aim is to observe the Markov discrete-time process of population growth with long-living trajectory. First we study asymptotical decay of generating function of Galton-Watson process for all cases as the Basic Lemma.…
A Galton-Watson process in a varying environment is a discrete time branching process where the offspring distributions vary among generations. It is known that in the critical case, these processes have a Yaglom limit, that is, a suitable…
We examine the population growth system called Q-processes. This is defined by the Galton-Watson Branching system conditioned on non-extinction of its trajectory in the remote future. In this paper we observe the total progeny up to time…
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…
A properly scaled critical Galton-Watson process converges to a continuous state critical branching process $\xi(\cdot)$ as the number of initial individuals tends to infinity. We extend this classical result by allowing for overlapping…
1 Sharp prediction of extinction times is needed in biodiversity monitoring and conservation management. 2 The Galton-Watson process is a classical stochastic model for describing population dynamics. Its evolution is like the matrix…
We study an iterated temporal and contemporaneous aggregation of $N$ independent copies of a strongly stationary subcritical Galton-Watson branching process with regularly varying immigration having index $\alpha \in (0, 2)$. Limits of…
Multi-type inhomogeneous Galton--Watson process with immigration is investigated, where the offspring mean matrix slowly converges to a critical mean matrix. Under general conditions we obtain limit distribution for the process, where the…
We consider a supercritical Galton-Watson branching process with immigration. It is well known that under suitable conditions on the offspring and immigration distributions, there is a finite, strictly positive limit ${\mathcal{W}}$ for the…