Related papers: Critical multitype branching: a functional limit t…
The aim of this paper is to study the fluctuations of a general class of supercritical branching Markov processes with non-local branching mechanisms. We show the existence of three regimes according to the size of the spectral gap…
We consider a branching random walk on $\mathbb{R}$ with a stationary and ergodic environment $\xi=(\xi_n)$ indexed by time $n\in\mathbb{N}$. Let $Z_n$ be the counting measure of particles of generation $n$. For the case where the…
A class of Fleming-Viot processes with decaying sampling rates and $\alpha$-stable motions that correspond to distributions with growing populations are introduced and analyzed. Almost sure long-time scaling limits for these processes are…
When a spatial process is recorded over time and the observation at a given time instant is viewed as a point in a function space, the result is a time series taking values in a Banach space. To study the spatio-temporal extremal dynamics…
A new formulation of non-local branching superprocesses is given from which we derive as special cases the rebirth, the multitype, the mass-structured, the multilevel and the age-reproduction-structured superprocesses and the…
Consider a branching process $\{Z_n\}_{n\ge 0}$ with immigration in varying environment. For $a\in\{0,1,2,...\},$ let $C=\{n\ge0:Z_n=a\}$ be the collection of times at which the population size of the process attains level $a.$ We give a…
We study branching Markov chains on a countable state space (space of types) $\mathscr{X}$, with the focus on the qualitative aspects of the limit behaviour of the evolving empirical population distributions. No conditions are imposed on…
Branching processes are classical growth models in cell kinetics. In their construction, it is usually assumed that cell lifetimes are independent random variables, which has been proved false in experiments. Models of dependent lifetimes…
Selection of descent direction at a point plays an important role in numerical optimization for minimizing a real valued function. In this article, a descent sequence is generated for the functions with bounded parameters to obtain a…
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…
Let $\left\{ Z_{n},n=0,1,2,...\right\} $ be a critical branching process in random environment and let $\left\{ S_{n},n=0,1,2,...\right\} $ be its associated random walk. It is known that if the increments of this random walk belong…
Branching processes form an important family of stochastic processes that have been successfully applied in many fields. In this paper, we focus our attention on controlled multi-type branching processes (CMBPs). A Feller-type diffusion…
The cell cycle duration is a variable cellular phenotype that underlies long-term population growth and age structures. By analyzing the stationary solutions of a branching process with heritable cell division times, we demonstrate…
We consider recurrent diffusive random walks on a strip. We present constructive conditions on Green functions of finite sub-domains which imply a Central Limit Theorem with polynomial error bound, a Local Limit Theorem, and mixing of…
We study the asymptotic behaviour of a properly normalized time-changed multidimensional Wiener process; the time change is given by an additive functional of the Wiener process itself. At the level of generators, the time change means that…
We consider a non-nestling random walk in a product random environment. We assume an exponential moment for the step of the walk, uniformly in the environment. We prove an invariance principle (functional central limit theorem) under almost…
We consider continuous-state branching processes (CB processes) which become extinct almost surely. First, we tackle the problem of describing the stationary measures on $(0,+\infty)$ for such CB processes. We give a representation of the…
By the methods of multitype branching processes in random environment counted by random characteristics we study the tail distribution of busy periods and some other characteristics of the branching type polling systems in which the service…
In this work, a generalised version of the central limit theorem is proposed for nonlinear functionals of the empirical measure of i.i.d. random variables, provided that the functional satisfies some regularity assumptions for the…
We consider the problem of estimating the parameters of a supercritical controlled branching process consistently from a single observed trajectory of population size counts. Our goal is to establish which parameters can and cannot be…