Related papers: Limit theorems for fragmentation processes with im…
In the spirit of a classical results for Crump-Mode-Jagers processes, we prove a strong law of large numbers for homogenous fragmentation processes. Specifically, for self-similar fragmentation processes, including homogenous processes, we…
Let $(Z_n)$ be a supercritical branching process with immigration in a random environment. The small positive values and some lower deviation inequalities for $Z$ are investigated. Based on these results, the central limit theorem of $\log…
We consider the limiting behavior of fluctuations of small noise diffusions with multiple scales around their homogenized deterministic limit. We allow full dependence of the coefficients on the slow and fast motion. These processes arise…
Under a fourth order moment condition on the branching and a second order moment condition on the immigration mechanisms, we show that an appropriately scaled projection of a supercritical and irreducible continuous state and continuous…
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…
We provide a simple set of sufficient conditions for the weak convergence of discrete Galton-Watson branching processes with immigration to continuous time and continuous state branching processes with immigration.
In this paper, we investigate the asymptotic behaviors of the critical branching process with immigration $\{Z_n, n\ge 0\}$. First we get some estimation for the probability generating function of $Z_n$. Based on it, we get a large…
This paper deals into the long-term behavior of subordinated critical branching processes with migration. We focus on scenarios where emigration is the dominant factor and introduce additional randomness in timing through a subordination…
We prove a general fluctuation limit theorem for Galton-Watson branching processes with immigration. The limit is a time-inhomogeneous OU type process driven by a spectrally positive Levy process. As applications of this result, we obtain…
We consider a branching random walk on $d$-dimensional real space with immigration in a time-dependent random environment. Let $Z_n(\mathbf t)$ be the so-called partition function of the process, namely, the moment generating function of…
We study the asymptotic behaviour of a critical decomposable 3-type Galton-Watson process with immigration when its offspring mean matrix is triangular with diagonal entries 1. It is proved that, under second or fourth order moment…
We study the asymptotic behavior of the weighted least squares estimators of the unknown parameters of bifurcating integer-valued autoregressive processes. Under suitable assumptions on the immigration, we establish the almost sure…
This paper demonstrates a new regeneration processes technology making use of positive stable distributions. We study the asymptotic behavior of branching processes with a randomly controlled migration component. Using the new method, we…
We consider a family of fragmentation processes where the rate at which a particle splits is proportional to a function of its mass. Let $F\_{1}^{(m)}(t),F\_{2}^{(m)}(t),...$ denote the decreasing rearrangement of the masses present at time…
Guided by the relationship between the breadth-first walk of a rooted tree and its sequence of generation sizes, we are able to include immigration in the Lamperti representation of continuous-state branching processes. We provide a…
We prove and extend some results stated by Mark Pinsky: Limit theorems for continuous state branching processes with immigration [Bull. Amer. Math. Soc. 78(1972), 242--244]. Consider a continuous-state branching process with immigration…
We consider a homogenous fragmentation process with killing at an exponential barrier. With the help of two families of martingales we analyse the growth of the largest fragment for parameter values that allow for survival. In this respect…
We consider a subcritical branching process in an i.i.d. random environment, in which one immigrant arrives at each generation. We consider the event $% \mathcal{A}_{i}(n)$ that all individuals alive at time $n$ are offspring of the…
We consider subcritical branching processes with immigration which evolve under the influence of a random environment and study the tail distribution of life periods of such processes defined as the length of the time interval between the…
In this paper the asymptotic behavior of a critical multi-type branching process with immigration is described when the offspring mean matrix is irreducible, in other words, when the process is indecomposable. It is proved that sequences of…