Related papers: Critical Controlled Branching Processes and Their …
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…
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 study asymptotic behavior of conditional least squares estimators for critical continuous state and continuous time branching processes with immigration based on discrete time (low frequency) observations.
We establish general sufficient conditions for a sequence of controlled branching processes to converge weakly on the Skorokhod space. We focus on a class of controlled random variables that extends previous results by considering them as a…
A discrete time branching process where the offspring distribution is generation-dependent, and the number of reproductive individuals is controlled by a random mechanism is considered. This model is a Markov chain but, in general, the…
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…
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…
We consider the genealogical tree of a stationary continuous state branching process with immigration. For a sub-critical stable branching mechanism, we consider the genealogical tree of the extant population at some fixed time and prove…
This article gives an overview of the developments in controlled diffusion processes, emphasizing key results regarding existence of optimal controls and their characterization via dynamic programming for a variety of cost criteria and…
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…
We consider a critical branching process $Y_{n}$ in an i.i.d. random environment, in which one immigrant arrives at each generation. Let $% \mathcal{A}_{i}(n)$ be the event that all individuals alive at time $n$ are offspring of the…
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…
Controlled branching processes are stochastic growth population models in which the number of individuals with reproductive capacity in each generation is controlled by a random control function. The purpose of this work is to examine the…
Branching processes form an important family of stochastic processes that have been successfully applied in many fields. In this paper, we focus our attention on controlled multi-type branching processes (CMBPs). A Feller-type diffusion…
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…
This paper is a collection of recent results on discrete-time and continuous-time branching random walks. Some results are new and others are known. Many aspects of this theory are considered: local, global and strong local survival, the…
The aim of this paper is to introduce a multitype branching process with random migration following the research initiated with the Galton-Watson process with migration introduced in [Yanev & Mitov (1980) C. R. Acad. Bulg. Sci.…
Under natural assumptions, a Feller type diffusion approximation is derived for critical, irreducible multi-type continuous state and continuous time branching processes with immigration. Namely, it is proved that a sequence of…
A branching process in varying environment with generation-dependent immigration is a modification of the standard branching process in which immigration is allowed and the reproduction and immigration laws may vary over the generations.…
A critical branching process with immigration which evolve in a random environment is considered. Assuming that immigration is not allowed when there are no individuals in the aboriginal population we investigate the tail distribution of…