George P. Yanev, Kosto V. Mitov, Nickolay M. Yanev
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 confirm some known results and establish new limit theorems that hold in a more general setting.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
继续探索
In this work, we give a description of all sigma-finite measures on the space of rooted compact real trees which satisfy a certain regenerative property. We show that any infinite measure which satisfies the regenerative property is the "law" of a Levy tree, that is, the "law" of a tree-valued random variable that describes the genealogy of a population evolving according to a continuous-state branching process. On the other hand, we prove that a probability measure with the regenerative property must be the law of the genealogical tree associated with a continuous-time discrete-state branchin…
We introduce regenerative tree growth processes as consistent families of random trees with n labelled leaves, n>=1, with a regenerative property at branch points. This framework includes growth processes for exchangeably labelled Markov branching trees, as well as non-exchangeable models such as the alpha-theta model, the alpha-gamma model and all restricted exchangeable models previously studied. Our main structural result is a representation of the growth rule by a sigma-finite dislocation measure kappa on the set of partitions of the natural numbers extending Bertoin's notion of exchangeab…
Continuous-state branching processes (CSBPs) with immigration (CBIs), stopped on hitting zero, are generalized by allowing the process governing immigration to be any Lévy process without negative jumps. Unlike the CBIs, these newly introduced processes do not appear to satisfy any natural affine property on the level of the Laplace transforms of the semigroups. Basic properties are noted. Explicit formulae (on neighborhoods of infinity) for the Laplace transforms of the first passage times downwards and of the explosion time are derived.
Critical Multitype Branching Processes with Random Migration
本文提出带随机迁移的临界多类型分支过程，给出无限增长的充分条件，研究规范化后的渐近分布，并建立 Feller 型扩散逼近。
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 introduced by Mandelbrot in 1972. We then show how very precise information about the zero sets of CBI can be obtained in terms of the branching and immigrating mechanism.
Long-Term Behavior of Subordinated Branching Processes with Prevailing Emigration
本文研究了具有主导移民的从属临界分支过程的长期行为，通过更新机制引入时间随机性，揭示了初始人口规模和到达间隔平均时间对非灭绝概率渐近行为及Yaglom型极限定理的影响，并探讨了交替再生过程，补充了移民主导移出过程的研究。
This survey aims at collecting and presenting results for one-type, discrete time branching processes with random control functions. In particular, the subclass of critical migration processes with different regimes of immigration and emigration is reviewed in detail. Critical controlled branching processes with continuous state space are also discussed.
We consider the long-time behaviour of a branching random walk in random environment on the lattice $\Z^d$. The migration of particles proceeds according to simple random walk in continuous time, while the medium is given as a random potential of spatially dependent killing/branching rates. The main objects of our interest are the annealed moments $< m_n^p > $, i.e., the $p$-th moments over the medium of the $n$-th moment over the migration and killing/branching, of the local and global population sizes. For $n=1$, this is well-understood \cite{GM98}, as $m_1$ is closely connected with the par…
We consider excited random walks on the integers with a bounded number of i.i.d. cookies per site which may induce drifts both to the left and to the right. We extend the criteria for recurrence and transience by M. Zerner and for positivity of speed by A.-L. Basdevant and A. Singh to this case and also prove an annealed central limit theorem. The proofs are based on results from the literature concerning branching processes with migration and make use of a certain renewal structure.
The occupation time of an age-dependent branching particle system in $\Rd$ is considered, where the initial population is a Poisson random field and the particles are subject to symmetric $α$-stable migration, critical binary branching and random lifetimes. Two regimes of lifetime distributions are considered: lifetimes with finite mean and lifetimes belonging to the normal domain of attraction of a $γ$-stable law, $γ\in(0,1)$. It is shown that in dimensions $d>αγ$ for the heavy-tailed lifetimes case, and $d>α$ for finite mean lifetimes, the occupation time proccess satisfies a strong law of l…
We consider a spatial branching process with emigration in which children either remain at the same site as their parents or migrate to new locations and then found their own colonies. We are interested in asymptotics of the partition of the total population into colonies for large populations with rare migrations. Under appropriate regimes, we establish weak convergence of the rescaled partition to some random measure that is constructed from the restriction of a Poisson point measure to a certain random region, and whose cumulant solves a simple integral equation.
A general multi-type population model is considered, where individuals live and reproduce according to their age and type, but also under the influence of the size and composition of the entire population. We describe the dynamics of the population density as a measure-valued process and obtain its asymptotics, as the population grows with the environmental carrying capacity. "Density" in this paper generally refers to the population size as compared to the carrying capacity. Thus, a deterministic approximation is given, in the form of a Law of Large Numbers, as well as a Central Limit Theorem…
Branching Processes in Random Environments with Thresholds
本文研究了具有阈值的随机环境分支过程，通过识别再生结构和极限分布，探讨了超临界和亚临界状态的持续时间和停留比例。
Structured coalescents, coagulation equations and multi-type branching processes
本文研究了结构人口中祖先谱系的凝聚过程，通过分析临界和大样本情形，发现经验测度过程收敛于d维凝聚方程的解，分别由多型分支过程和进入法表示。
Continuous-state branching processes with collisions: first passage times and duality
该研究引入带随机碰撞的连续状态分支过程（CBCs），证明其为唯一满足半直线一维扩散拉普拉斯对偶的无负跳Feller过程，推导了边界吸引性、极限分布、首达时拉普拉斯变换及非爆炸条件。
Occupation time fluctuations of an age-dependent critical binary branching particle system
本文研究年龄依赖临界二元分支粒子系统占据时间过程的极限波动，针对有限期望和帕累托型寿命分布，证明了弱收敛于加权子分数布朗运动，并探讨其性质与参数范围。
Two-type branching processes with immigration, and the structured coalescents
本文研究了两种类型个体在两个岛屿上的分支过程，通过两型Feller扩散模型探讨了频率变化，并推导了不对称两岛频率过程的性质及大种群极限，揭示了平衡选择的新机制。
扫码添加微信好友，提出您的宝贵建议 👇
💡 备注请填写：网站反馈
发表机构由 AI 从论文文本抽取，如发现错误，欢迎反馈修正建议。