Related papers: Extinction properties of multi-type continuous-sta…
In [Aldous,Pitman,1998] a tree-valued Markov chain is derived by pruning off more and more subtrees along the edges of a Galton-Watson tree. More recently, in [Abraham,Delmas,2012], a continuous analogue of the tree-valued pruning dynamics…
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…
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…
Consider a continuous-state branching population constructed as a flow of nested subordinators. Inverting the subordinators and reversing time give rise to a flow of coalescing Markov processes (with negative jumps) which correspond to the…
We provide a new proof for regularity of affine processes on general state spaces by methods from the theory of Markovian semimartingales. On the way to this result we also show that the definition of an affine process, namely as…
Functional limit theorems are established for continuous-state branching processes with immigration (CBIs), where the reproduction laws have finite first moments and the immigration laws exhibit large tails. Different regimes of immigration…
In this paper, we introduce a class of processes that contains many natural examples. The interesting feature of such type processes lays on its infinite memory that allows it to record a quite ancient history. Then, using the martingale…
A class of branching processes in varying environments is exhibited which become extinct almost surely even though the means M_n grow fast enough so that sum M_n^{-1} is finite. In fact, such a process is constructed for every offspring…
We start by providing an explicit characterization and analytical properties, including the persistence phenomena, of the distribution of the extinction time $\mathbb{T}$ of a class of non-Markovian self-similar stochastic processes with…
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…
We study properties of a $p-$type subcritical branching process in random environment initiated at moment zero by a vector $\mathbf{z}=\left( z_{1},..,z_{p}\right) $\ of particles of different types. Assuming that the process belongs to the…
We establish sufficient conditions for exponential convergence to a unique quasi-stationary distribution in the total variation norm. These conditions also ensure the existence and exponential ergodicity of the Q-process, the process…
Bifurcating Markov chains (BMC) are Markov chains indexed by a full binary tree representing the evolution of a trait along a population where each individual has two children. We provide a central limit theorem for general additive…
By decomposing the random walk path, we construct a multitype branching process with immigration in random environment for corresponding random walk with bounded jumps in random environment. Then we give two applications of the branching…
This paper features a Cram\'er's theorem for finite-state Markov chains indexed by rooted $d$-trees, obtained via the method of types in the classical analysis of large deviations. Along with the theorem comes two applications: an…
We reconsider the deterministic haploid mutation-selection equation with two types. This is an ordinary differential equation that describes the type distribution (forward in time) in a population of infinite size. This paper establishes…
We observe the continuous-time Markov Branching Process without high-order moments and allowing Immigration. Limit properties of transition functions and their convergence to invariant measures are investigated. Main mathematical tool is…
Under a fourth order moment condition on the branching and a second order moment condition on the immigration mechanisms, we show that an appropriately scaled projection of a supercritical and irreducible continuous state and continuous…
We first derive the recurisions for integer moments of two-type continuous-state branching processes in L\'{e}vy random environments. Result shows that the $n$th moment of the process is a polynomial of the initial value of the process with…
We establish the exponential ergodic property in a weighted total variation distance of continuous-state branching processes with immigration in random environments with competition and catastrophes, under a Lyapunov-type condition and…