Related papers: Reinforced Galton--Watson processes III: Empirical…

We are interested in the evolving genealogy of a birth and death process with trait structure and ecological interactions. Traits are hereditarily transmitted from a parent to its offspring unless a mutation occurs. The dynamics may depend…

Several populational networks present complex topologies when implemented in evolutionary algorithms. A common feature of these topologies is the emergence of a power law. Power law behavior with different scaling factors can also be…

In this paper the Galton Watson branching process has been studied for a class of offspring distributions which are in a way sandwiched between the Bernoulli and Poisson.

This paper proposes a novel numerical method for computing the density of the limit random variable associated with a supercritical Galton-Watson process. This random variable captures the effect of early demographic fluctuations and…

Event-driven systems in fields such as neuroscience, social networks, and finance often exhibit dynamics influenced by continuously evolving external covariates. Motivated by these applications, we introduce a new class of multivariate…

We consider stochastic dynamics of a population which starts from a small colony on a habitat with large but limited carrying capacity. A common heuristics suggests that such population grows initially as a Galton-Watson branching process…

In this paper introduces a new family of continuous distributions namely the Poison transmuted-G family of distribution is proposed by inducing two addition parameter on the base line G distribution. Some of its mathematical properties…

In this paper we study random partitions of 1,...n, where every cluster of size j can be in any of w\_j possible internal states. The Gibbs (n,k,w) distribution is obtained by sampling uniformly among such partitions with k clusters. We…

Repetitions within a given genealogical tree provides some information about the degree of consanguineity of a population. They can be analyzed with techniques usually employed in statistical physics when dealing with fixed point…

In this paper the asymptotic behaviour of a critical 2-type Galton-Watson process with immigration is described when its offspring mean matrix is reducible, in other words, when the process is decomposable. It is proved that, under second…

Gaussian processes (GPs) are a powerful tool for probabilistic inference over functions. They have been applied to both regression and non-linear dimensionality reduction, and offer desirable properties such as uncertainty estimates,…

Widely used models in genetics include the Wright-Fisher diffusion and its moment dual, Kingman's coalescent. Each has a multilocus extension but under neither extension is the sampling distribution available in closed-form, and their…

We consider an indecomposable Galton-Watson branching process with countably infinitely many types. Assuming that the process is critical and allowing for infinite variance of the offspring sizes of some (or all) types of particles we…

We derive the asymptotic behaviour of the genealogy of a logistic branching process in the setting where the equilibrium population size is large. In three regimes on the tail of the offspring distribution we recover the Kingman,…

We provide a generalization of Theorem 1 in Bartkiewicz, Jakubowski, Mikosch and Wintenberger (2011) in the sense that we give sufficient conditions for weak convergence of finite dimensional distributions of the partial sum processes of a…

The models surveyed include generalized P\'{o}lya urns, reinforced random walks, interacting urn models, and continuous reinforced processes. Emphasis is on methods and results, with sketches provided of some proofs. Applications are…

We consider a population of particles with unit life length. Dying each particle produces offspring whose size depends on the random environment specifying the reproduction law of all particles of the given generation and on the number of…

We consider branching random walks and contact processes on infinite, connected, locally finite graphs whose reproduction and infectivity rates across edges are inversely proportional to vertex degree. We show that when the ambient graph is…

We show that the number of copies of a given rooted tree in a conditioned Galton-Watson tree satisfies a law of large numbers under a minimal moment condition on the offspring distribution.

We introduce a one-dimensional random walk, which at each step performs a reinforced dynamics with probability $\theta$ and with probability $1 - \theta$, the random walk performs a step independent of the past. We analyse its asymptotic…