Related papers: Moments, moderate and large deviations for a branc…

In this paper we establish spatial central limit theorems for a large class of supercritical branching Markov processes with general spatial-dependent branching mechanisms. These are generalizations of the spatial central limit theorems…

We consider branching processes for structured populations: each individual is characterized by a type or trait which belongs to a general measurable state space. We focus on the supercritical recurrent case, where the population may…

The asymptotic behavior, as $n\rightarrow \infty $ of the probability of the event that a decomposable critical branching process $\mathbf{Z}(m)=(Z_{1}(m),...,Z_{N}(m)),$ $m=0,1,2,...,$ with $N$ types of particles dies at moment $n$ is…

We consider branching random walks in $d$-dimensional integer lattice with time-space i.i.d. offspring distributions. When $d \ge 3$ and the fluctuation of the environment is well moderated by the random walk, we prove a central limit…

In this paper, we study second order fluctuations for the size of the range of a critical branching random walk (BRW) in $\mathbb Z^d$. We consider the BRW with geometric offspring indexed by the Kesten tree, and show that the size of its…

We consider a supercritical Galton-Watson branching process with immigration. It is well known that under suitable conditions on the offspring and immigration distributions, there is a finite, strictly positive limit ${\mathcal{W}}$ for the…

Let (Zn) be a branching process with immigration in an independent and identically distributed random environment. Under necessary moment conditions, we show the exact convergence rate in the central limit theorem on logZn by using the…

We consider a particle system in continuous time, discrete population, with spatial motion and nonlocal branching. The offspring's weights and their number may depend on the mother's weight. Our setting captures, for instance, the processes…

We consider a random walk on $\Z$ that branches at the origin only. In the supercritical regime we establish a law of large number for the maximal position $M_n$. Then we determine all possible limiting law for the sequence $M_n -\alpha n$…

Let $\boldsymbol W=\{\boldsymbol W_n:n\in\mathbb N\}$ be a sequence of random vectors in $\mathbb R^d$, $d\ge 1$. This paper considers the logarithmic asymptotics of the extremes of $\boldsymbol W$, that is, for any vector $\boldsymbol…

Let $T$ be the extinction moment of a critical branching process $Z=(Z_{n},n\geq 0) $ in a random environment specified by iid probability generating functions. We study the asymptotic behavior of the probability of extinction of the…

We study supercritical age-structured branching models starting from a single particle with a random lifetime, where the reproduction law depends on the remaining lifetime of the parent. The lifespan of an individual is decided at its birth…

We study the large deviation behaviour of $S_n=\sum_{j=1}^n W_jZ_j$, where $(W_j)_{j \in \mathbb N}$ and $(Z_j)_{j \in \mathbb N}$ are sequences of real-valued, independent and identically distributed random variables satisfying certain…

In this work we investigate limit theorems for the time-averaged process $\left(\frac{1}{t}\int_0^t X_s^x ds\right)_{t\geq 0}$ where $X^x$ is a subcritical continuous-state branching processes with immigration (CBI processes) starting in $x…

We consider the branching random walk drifting to $-\infty$ and we investigate large deviations-type estimates for the first passage time. We prove the corresponding law of large numbers and the central limit theorem.

We consider the adjacency matrix $A$ of a large random graph and study fluctuations of the function $f_n(z,u)=\frac{1}{n}\sum_{k=1}^n\exp\{-uG_{kk}(z)\}$ with $G(z)=(z-iA)^{-1}$. We prove that the moments of fluctuations normalized by…

In this paper we consider two branching processes living in a joint random environment. Assuming that both processes are critical we address the following question: What is the probability that both populations survive up to a large time…

Consider a population of individuals belonging to an infinity number of types, and assume that type proportions follow the two-parameter Poisson-Dirichlet distribution. A sample of size n is selected from the population. The total number of…

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…

Let $\{Z_{1,n} , n\geq 0\}$ and $\{Z_{2,n}, n\geq 0\}$ be two supercritical branching processes in different random environments, with criticality parameters $\mu_1$ and $\mu_2$ respectively. It is known that $\frac{1}{n} \ln Z_{1,n}…