Related papers: On the Limit Distributions of Continuous-State Bra…
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…
Continuous-state branching processes (CSBPs) with immigration (CBIs), stopped on hitting zero, are generalized by allowing the process governing immigration to be any L\'evy process without negative jumps. Unlike the CBIs, these newly…
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 study the estimation of two-type continuous-state branching processes with immigration (CBI-processes). The ergodicity of the processes is proved. We also establish the strong consistency and central limit theorems of the conditional…
Functional limit theorems are established for continuous-state branching processes with immigration (CBIs), where the reproduction laws have finite first moments and the immigration laws exhibit large tails. Different regimes of immigration…
The purpose of this article is to observe that the zero sets of continuous-state branching processes with immigration (CBI) are infinitely divisible regenerative sets. Indeed, they can be constructed by the procedure of random cutouts…
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…
This work provides a brief introduction to continuous-state branching processes (CB-processes) and continuous-state branching processes with immigration (CBI-processes) accessible to graduate students with reasonable background in…
Under a first order moment condition on the immigration mechanism, we show that an appropriately scaled supercritical and irreducible multi-type continuous state and continuous time branching process with immigration (CBI process) converges…
We study the distributional properties of jumps of multi-type continuous state and continuous time branching processes with immigration (multi-type CBI processes). We derive an expression for the distribution function of the first jump time…
In this paper, we study continuous-state interacting multi-type branching processes with immigration (CIMBI processes), where inter-specific interactions -- whether competitive, cooperative, or of a mixed type -- are proportional to the…
We construct a continuous state branching process with immigration (CBI) whose immigration depends on the CBI itself and we recover a continuous state branching process (CB). This provides a dual construction of the pruning at nodes of CB…
We consider a multitype branching process with immigration in a random environment introduced by Key in [Ann. Probab. 15 (1987) 344--353]. It was shown by Key that, under the assumptions made in [Ann. Probab. 15 (1987) 344--353], the…
A Galton-Watson branching process with immigration evolving in a random environment is considered. Its associated random walk is assumed to be oscillating. We prove a functional limit theorem in which the process under consideration is…
We derive an expression for the joint distribution function of the first jump times of a continuous state and continuous time branching process with immigration (CBI process) with jump sizes in given Borel sets having finite total L\'evy…
We introduce and study the class of CBI-time-changed L\'evy processes (CBITCL), obtained by time-changing a L\'evy process with respect to an integrated continuous-state branching process with immigration (CBI). We characterize CBITCL…
In this work we investigate limit theorems for the time-averaged process $\left(\frac{1}{t}\int_0^t X_s^x ds\right)_{t\geq 0}$ where $X^x$ is a subcritical continuous-state branching processes with immigration (CBI processes) starting in $x…
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 determine the tail asymptotics of the stationary distribution of a branching process with immigration in a random environment, when the immigration distribution dominates the offspring distribution. The assumptions are the same as in the…
We investigate subcritical Galton-Watson branching processes with immigration in a random environment. Using Goldie's implicit renewal theory we show that under general Cram\'er condition the stationary distribution has a power law tail. We…