Related papers: On functional limit theorems for branching process…
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 system of multiscale stochastic differential equations whose slow component is drivenby a fractional Brownian motion with Hurst parameter H greater than 1/2. Under ergodic assumptions ensuring the applicability of the…
We consider a family of general branching processes with reproduction parameters depending on the age of the individual as well as the population age structure and a parameter $K$, which may represent the carrying capacity. These processes…
Using a population dynamics inspired by an ensemble of growing cells, a set of fluctuation theorems linking observables measured at the lineage and population levels are derived. One of these relations implies specific inequalities…
This survey aims at collecting and presenting results for one-type, discrete time branching processes with random control functions. In particular, the subclass of critical migration processes with different regimes of immigration and…
A special type of immigration associated with measure-valued branching processes is formulated by using skew convolution semigroups. We give characterization for a general inhomogeneous skew convolution semigroup in terms of probability…
We study fluctuations of the empirical processes of a non-equilibrium interacting particle system consisting of two species over a domain that is recently introduced in [8] and establish its functional central limit theorem. This…
A second-order Galton-Watson process with immigration can be represented as a coordinate process of a 2-type Galton-Watson process with immigration. Sufficient conditions are derived on the offspring and immigration distributions of a…
We consider a limit theorem for a triangular array of point processes generated by non-identically distributed random variables, and apply the result for the analysis of the limiting behavior of the Argmaximum of independent random…
This work considers a type of slow-fast system, where the slow component is driven by fractional Brownian motion with H > 1/2 and the fast component is a Markovian stationary process. Our solution mapping is defined based on the…
Let $(W_{t}(\lambda))_{t\ge 0}$, parametrized by $\lambda\in\mathbb{R}$, be the additive martingale related to a supercritical super-Brownian motion on the real line and let $W_{\infty}(\lambda)$ be its limit. Under a natural condition for…
In this work we study the long-time behavior for subcritical measure-valued branching processes with immigration on the space of tempered measures. Under some reasonable assumptions on the spatial motion, the branching and immigration…
We prove the existence and pathwise uniqueness of the solution to a stochastic integral equation driven by Poisson random measures based on Kuznetsov measures for a continuous-state branching process. That gives a direct construction of the…
We prove a functional central limit theorem for partial sums of symmetric stationary long range dependent heavy tailed infinitely divisible processes with a certain type of negative dependence. Previously only positive dependence could be…
We construct extensions of the pure-jump $\Lambda$-Wright-Fisher processes with frequency-dependent selection ($\Lambda$-WF processes with selection) beyond their first passage time at the boundary $1$. We show that they satisfy some…
We aim to generalize the homogenisation theorem in \cite{Gehringer-Li-tagged} for a passive tracer interacting with a fractional Gau{\ss}ian noise to also cover fractional non-Gau{\ss}ian noises. To do so we analyse limit theorems for…
We investigate the limit behavior of supercritical multitype branching processes in random environments with linear fractional offspring distributions and show that there exists a phase transition in the behavior of local probabilites of…
A critical branching process $\left\{ Z_{k},k=0,1,2,...\right\} $ in a random environment is considered. A conditional functional limit theorem for the properly scaled process $\left\{ \log Z_{pu},0\leq u<\infty \right\} $ is established…
We study the global fluctuations for a class of determinantal point processes coming from large systems of non-colliding processes and non-intersecting paths. Our main assumption is that the point processes are constructed by biorthogonal…
We introduce a variational theory for processes adapted to the multi-dimensional Brownian motion filtration. The theory provides a differential structure which describes the infinitesimal evolution of Wiener functionals at very small…