Related papers: Branching Processes -- A General Concept

This work focuses on a class of regime-switching jump diffusion processes with a countably infinite state space for the discrete component. Such processes can be used to model complex hybrid systems in which both structural changes, small…

Neural network approaches for meta-learning distributions over functions have desirable properties such as increased flexibility and a reduced complexity of inference. Building on the successes of denoising diffusion models for generative…

After learning a concept, humans are also able to continually generalize their learned concepts to new domains by observing only a few labeled instances without any interference with the past learned knowledge. In contrast, learning…

We consider uniform random permutations drawn from a family enumerated through generating trees. We develop a new general technique to establish a central limit theorem for the number of consecutive occurrences of a fixed pattern in such…

We introduce Functional Diffusion Processes (FDPs), which generalize score-based diffusion models to infinite-dimensional function spaces. FDPs require a new mathematical framework to describe the forward and backward dynamics, and several…

We give a substitute to Feller property for semigroups of time-changed processes; under some conditions this leads to establish sufficient (new) conditions for the semigroups to be Feller. Moreover, given a standard process and a sequence…

A multi-type branching process is defined as a random tree with labeled vertices, where each vertex produces offspring independently according to the same multivariate probability distribution. We demonstrate that in realizations of the…

Let U be an open set in R^d. We show that under a mild assumption on the richness of the generator a Feller process in U with (predictable) killing is a semimartingale. To this end we generalize the notion of semimartingales in a natural…

The linear-fractional Galton-Watson processes is a well known case when many characteristics of a branching process can be computed explicitly. In this paper we extend the two-parameter linear-fractional family to a much richer…

Homogeneous mass fragmentation processes describe the evolution of a unit mass that breaks down randomly into pieces as time. Mathematically speaking, they can be thought of as continuous-time analogues of branching random walks with…

Consider a multi-dimensional supercritical branching process with offspring distribution in a parametric family. Here, each vector coordinate corresponds to the number of offspring of a given type. The process is observed under family-size…

(Multi-type) branching processes are a natural and well-studied model for generating random infinite trees. Branching processes feature both nondeterministic and probabilistic branching, generalizing both transition systems and Markov…

In branching process theory, linear-fractional distributions are commonly used to model individual reproduction, especially when the goal is to obtain more explicit formulas than those derived under general model assumptions. In this…

We consider a continuous-time branching random walk on $\mathbb{Z}$ in a random non homogeneous environment. Particles can walk on the lattice points or disappear with random intensities. The process starts with one particle at initial time…

We present a simple construction method for Feller processes and a framework for the generation of sample paths of Feller processes. The construction is based on state space dependent mixing of L\'evy processes. Brownian Motion is one of…

Motivated by a recently proposed design for a DNA coded randomised algorithm that enables inference of the average generation of a collection of cells descendent from a common progenitor, here we establish strong convergence properties for…

It is possible to consider stochastic models of sequence evolution in phylogenetics in the context of a dynamical tensor description inspired from physics. Approaching the problem in this framework allows for the well developed methods of…

For a branching process in random environment it is assumed that the offspring distribution of the individuals varies in a random fashion, independently from one generation to the other. Interestingly there is the possibility that the…

In this article, we study the extremal processes of branching Brownian motions conditioned on having an unusually large maximum. The limiting point measures form a one-parameter family and are the decoration point measures in the extremal…

While classical concentration inequalities are typically restricted to two special cases -- independence and martingale difference sequences -- we extend concentration inequalities to a much broader class of stochastic processes by relaxing…