Related papers: Limit Theorems for Some Critical Superprocesses

We prove a Functional Central Limit Theorem for the position of a Tagged Particle in the one-dimensional Asymmetric Simple Exclusion Process in the hyperbolic scaling, starting from a Bernoulli product measure conditioned to have a particle…

Central limit theorems are established for the sum, over a spatial region, of observations from a linear process on a $d$-dimensional lattice. This region need not be rectangular, but can be irregularly-shaped. Separate results are…

We prove a law of large numbers and a central limit theorem for a tagged particle in a symmetric simple exclusion process in the one-dimensional lattice with variable diffusion coefficient. The scaling limits are obtained from a similar…

Conditions for almost sure extinction are studied in discrete time branching processes with an infinite number of types. It is not assumed that the expected number of children is a bounded function of the parent's type. There might also be…

We are interested in a fragmentation process. We observe fragments frozen when their sizes are less than $\epsilon$ ($\epsilon$ > 0). Is is known ([BM05]) that the empirical measure of these fragments converges in law, under some…

We study inhomogeneous random graphs with a finite type space. For a natural generalization of the model as a dynamic network-valued process, the paper establishes the following results: (a) Functional central limit theorems for the…

In this article, we consider a sequence $(N_n)_{n \geq 1}$ of point processes, whose points lie in a subset $E$ of $\bR \verb2\2 \{0\}$, and satisfy an asymptotic independence condition. Our main result gives some necessary and sufficient…

Let $X=(X_t, t\geq 0)$ be a superprocess in a random environment described by a Gaussian noise $W=\{W(t,x), t\geq 0, x\in \mathbb{R}^d\}$ white in time and colored in space with correlation kernel $g(x,y)$. When $d\geq 3$, under the…

We consider a positive recurrent one-dimensional diffusion process with continuous coefficients and we establish stable central limit theorems for a certain type of additive functionals of this diffusion. In other words we find some…

Let $\{(X_t)_{t\geq 0}, \mathbb{P}_{\delta_x}, x\in E\}$ be a supercritical branching Markov process (which is not necessary symmetric) on a locally compact metric measure space $(E,\mu)$ with spatially dependent local branching mechanism.…

Let $W_t(\theta)$ be the Biggins martingale of a supercritical branching L\'evy process with non-local branching mechanism, and denote by $W_\infty(\theta)$ its limit. In this paper, we first study moment properties of $W_t(\theta)$ and…

Lower and upper bounds for the cumulative distribution function (cdf) of the time to extinction in a subcritical two-sex branching process are derived. A recursive procedure for approximating this cdf is also utilized. The results are…

In this paper, a very useful lemma (in two versions) is proved: it simplifies notably the essential step to establish a Lindeberg central limit theorem for dependent processes. Then, applying this lemma to weakly dependent processes…

It is well known that a simple, supercritical Bienaym\'e-Galton-Watson process turns into a subcritical such process, if conditioned to die out. We prove that the corresponding holds true for general, multi-type branching, where…

For supercritical multitype branching processes in continuous time, we investigate the evolution of types along those lineages that survive up to some time t. We establish almost-sure convergence theorems for both time and population…

We establish a Law of Large Numbers and a Central Limit Theorem for a class of Crump Mode Jagers continuous time branching processes, where the birth rate is age dependent, and also random (different from one individual to the next), in the…

We investigate extreme value theory for physical systems with a global conservation law which describe renewal processes, mass transport models and long-range interacting spin models. As shown previously, a special feature is that the…

Limit theorems of strong law of large numbers and central limit theorem types are obtained for the compositions of independent identically distributed random unitary channels.

In this article, we quantify the functional convergence of the rescaled random walk with heavy tails to a stable process.This generalizes the Generalized Central Limit Theorem for stable random variables infinite dimension. We show that…

Extinction times in resampling processes are fundamental yet often intractable, as previous formulas scale as $2^M$ with the number of states $M$ present in the initial probability distribution. We solve this by treating multinomial updates…