Related papers: Approximation of the Height process of a CSBP with…
We study the long-term behavior of weighted multi-type branching processes, focusing on extending classical laws of large numbers and martingale convergence to settings with infinitely many weighted particles, arbitrary type spaces and…
Stochastic Approximation (SA) is a widely used algorithmic approach in various fields, including optimization and reinforcement learning (RL). Among RL algorithms, Q-learning is particularly popular due to its empirical success. In this…
We consider population-size-dependent branching processes (PSDBPs) which eventually become extinct with probability one. For these processes, we derive maximum likelihood estimators for the mean number of offspring born to individuals when…
We are interested in modelling Darwinian evolution, resulting from the interplay of phenotypic variation and natural selection through ecological interactions. Our models are rooted in the microscopic, stochastic description of a population…
Consider a stochastic process that behaves as a $d$-dimensional simple and symmetric random walk, except that, with a certain fixed probability, at each step, it chooses instead to jump to a given site with probability proportional to the…
We survey results on the description of stochastically evolving genealogies of populations and marked genealogies of multitype populations or spatial populations via tree-valued Markov processes on (marked) ultrametric measure spaces. In…
Recent literature suggests that the bigger the model, the more likely it is to converge to similar, ``universal'' representations, despite different training objectives, datasets, or modalities. While this literature shows that there is an…
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 refine previous results concerning the Renewal Contact Processes. We significantly widen the family of distributions for the interarrival times for which the critical value can be shown to be strictly positive. The result now holds for…
Interacting particle systems undergoing repeated mutation and selection steps model genetic evolution, and also describe a broad class of sequential Monte Carlo methods. The genealogical tree embedded into the system is important in both…
We introduce a model of a randomly growing interface in multidimensional Euclidean space. The growth model incorporates a random order model as an ingredient of its graphical construction, in a way that replicates the connection between the…
Random critical branching trees (CBTs) are generated by the multiplicative branching process, where the branching number is determined stochastically, independent of the degree of their ancestor. Here we show analytically that despite this…
Bayesian inference is now a leading technique for reconstructing phylogenetic trees from aligned sequence data. In this short note, we formally show that the maximum posterior tree topology provides a statistically consistent estimate of a…
We consider a one-dimensional dyadic branching Brownian motion on $\mathbb{R}$ with positive drift $\beta \in (0,1)$, branching rate $1/2$, reflected at $0$ and killed at a boundary $L > 0$. The killing boundary $L$ is chosen so that the…
We introduce an architecture for large-scale image categorization that enables the end-to-end learning of separate visual features for the different classes to distinguish. The proposed model consists of a deep CNN shaped like a tree. The…
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…
In this work we model the dynamics of a population that evolves as a continuous time branching process with a trait structure and ecological interactions in form of mutations and competition between individuals. We generalize existing…
The problem of conditioning a continuous-state branching process with quadratic competition (logistic CB process) on non-extinction is investigated. We first establish that non-extinction is equivalent to the total progeny of the population…
Interacting particle systems can often be constructed from a graphical representation, by applying local maps at the times of associated Poisson processes. This leads to a natural coupling of systems started in different initial states. We…
In a population with haploid reproduction any individual has a single parent in the previous generation. If all genealogical distances among pairs of individuals (generations from the closest common ancestor) are known it is possible to…