相关论文: Revisiting Offspring Maxima in Branching Processes
In 2022, we published the book Maximum-Entropy Sampling: Algorithms and Application (Springer). Since then, there have been several notable advancements on this topic. In this manuscript, we survey some recent highlights.
The theory of evolutionary computation for discrete search spaces has made significant progress in the last ten years. This survey summarizes some of the most important recent results in this research area. It discusses fine-grained models…
We consider a broad class of continuous-time two-type population size-dependent Markov Branching Processes. The offspring distribution can depend on the current (alive) and total (dead and alive) populations. Using stochastic approximation…
Consider a branching process with a homogeneous reproduction law. Sampling a single cell uniformly from the population at a time $T > 0$ and looking along the sampled cell's ancestral lineage, we find that the reproduction law is…
We study a class of branching processes in which a population consists of immortal individuals equipped with a fitness value. Individuals produce offspring with a rate given by their fitness, and offspring may either belong to the same…
Ancestral inference for branching processes in random environments involves determining the ancestor distribution parameters using the population sizes of descendant generations. In this paper, we introduce a new methodology for ancestral…
In this paper, we review recent results of ours concerning branching processes with general lifetimes and neutral mutations, under the infinitely many alleles model, where mutations can occur either at birth of individuals or at a constant…
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…
Consider a continuous-time binary branching process conditioned to have population size n at some time t, and with a chance p for recording each extinct individual in the process. Within the family tree of this process, we consider the…
We consider branching Brownian motion in which initially there is one particle at $x$, particles produce a random number of offspring with mean $m+1$ at the time of branching events, and each particle branches at rate $\beta = 1/2m$.…
We provide a fundamental result for bucket increasing trees, which gives a complete characterization of all families of bucket increasing trees that can be generated by a tree evolution process. We also provide several equivalent…
The long-term behaviors of flows of continuous-state branching processes are characterized through subordinators and extremal processes. The extremal processes arise in the case of supercritical processes with infinite mean and of…
Results on the behaviour of the rightmost particle in the $n$th generation in the branching random walk are reviewed and the phenomenon of anomalous spreading speeds, noticed recently in related deterministic models, is considered. The…
Let X be a critical branching L{\'e}vy process whose offspring distribution is in the domain of attraction of a stable random variable. We study the tail probability of the maximum location ever reached by a particle in two different…
This article examines a recent body of work on stochastic processes indexed by a tree. Emphasis is on the application of this new framework to existing probability models. Proofs are largely omitted, with references provided.
This review paper presents the known results on the asymptotics of the survival probability and limit theorems conditioned on survival of critical and subcritical branching processes in IID random environments. The key assumptions of the…
We continue our study of the distribution of the maximal number $X^{\ast}_k$ of offsprings amongst all individuals in a critical Galton-Watson process started with $k$ ancestors, treating the case when the reproduction law has a regularly…
We study time continuous branching processes with exponentially distributed lifetimes, with two types of cells that proliferate according to binary fission. A range of possible system dynamics are considered, each of which is characterized…
We derive an exact expression for the probability density function of the cascade size (total progeny) in a continuous state branching process when the generations are Gamma distributed. The distribution has application in the modelling of…
We investigate branching processes in nearly degenerate varying environment, where the offspring distribution converges to the degenerate distribution at 1. Such processes die out almost surely, therefore, we condition on non-extinction or…