Related papers: On functional limit theorems for branching process…
In this paper, we study the weak convergence of the extremes of supercritical branching L\'evy processes $\{\mathbb{X}_t, t \ge0\}$ whose spatial motions are L\'evy processes with regularly varying tails. The result is drastically different…
Current fluctuations in boundary-driven diffusive systems are, in many cases, studied using hydrodynamic theories. Their predictions are then expected to be valid for currents which scale inversely with the system size. To study this…
We establish limit theorems involving weak convergence of multiple generations of critical and supercritical branching processes. These results arise naturally when dealing with the joint asymptotic behavior of functionals defined in terms…
We consider a continuous-time symmetric branching random walk on multidimensional lattices with immigration and infinite number of initial particles. We assume that at every lattice point a process of birth and death of particles is…
We explore fluctuation relations in a periodically driven micromechanical torsional oscillator. In the linear regime where the modulation is weak, we verify that the ratio of the work variance to the mean work is constant, consistent with…
We consider the fluctuations of regular functions $f$ of a Wigner matrix $W$ viewed as an entire matrix $f(W)$. Going beyond the well studied tracial mode, $\mathrm{Tr}[f(W)]$, which is equivalent to the customary linear statistics of…
Under certain mild conditions, some limit theorems for functionals of two independent Gaussian processes are obtained. The results apply to general Gaussian processes including fractional Brownian motion, sub-fractional Brownian motion and…
We study the asymptotic behavior of empirical processes generated by measurable bounded functions of an infinite source Poisson transmission process when the session length have infinite variance. In spite of the boundedness of the…
In his, by now, classical work from 1981, Nerman made extensive use of a crucial martingale $(W_t)_{t \geq 0}$ to prove convergence in probability, in mean and almost surely, of supercritical general branching processes (a.k.a.…
We consider a family of fragmentation processes where the rate at which a particle splits is proportional to a function of its mass. Let $F\_{1}^{(m)}(t),F\_{2}^{(m)}(t),...$ denote the decreasing rearrangement of the masses present at time…
We establish an explicit rate of convergence for some systems of mean-field interacting diffusions with logistic binary branching towards the solutions of nonlinear evolution equations with non-local self-diffusion and logistic mass growth,…
In this paper, we consider $n$-type Markov branching processes with immigration and resurrection. The uniqueness criteria are first established. Then, a new method is found and the explicit expression of extinction probability is…
We study the small-time fluctuations for diffusion processes which are conditioned by their initial and final positions, under the assumptions that the diffusivity has a sub-Riemannian structure and that the drift vector field lies in the…
A Markov process fluctuating away from its typical behavior can be represented in the long-time limit by another Markov process, called the effective or driven process, having the same stationary states as the original process conditioned…
Analytical solutions for time-inhomogeneous linear birth-death processes with immigration are derived. While time-inhomogeneous linear birth-death processes without immigration have been studied by using a generating function approach, 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 establish recurrence and transience criteria for critical branching processes in random environment with immigration. These results are then applied to discuss recurrence and transience of a recurrent random walk in a random environment…
For a positive continuous function f satisfying some standard conditions, we study the f-moments of continuous-state branching processes with or without immigration. The main results give criteria for the existence of the f-moments. The…
Continuous state branching processes with immigration are studied. We are particularly concerned with the associated (non-symmetric) Dirichlet form. After observing that gamma distributions are only reversible distributions for this class…
Life is on the razor's edge as resulting from competitive birth and death random forces. We illustrate this aphorism in the context of three Markov chain population models where systematic random immigration events promoting growth are…