Related papers: Central Limit Theorems for Supercritical Branching…
Two time scale stochastic approximation algorithms emulate singularly perturbed deterministic differential equations in a certain limiting sense, i.e., the interpolated iterates on each time scale approach certain differential equations in…
We prove a central limit type theorem for critical marked Hawkes processes. We study the case where the marks are i.i.d. with nonnegative values and their common distribution is either heavy tailed or has finite variance. The kernel…
We study sufficient conditions for the belonging of random process to certain Besov space and for the Central Limit Theorem (CLT) in these spaces. We investigate also the non-asymptotic tail behavior of normed sums of centered random…
We consider the cardinality of supercritical oriented bond percolation in two dimensions. We show that, whenever the origin is conditioned to percolate, the process appropriately normalized converges asymptotically in distribution to the…
In this paper we obtain the central limit theorem for triangular arrays of non-homogeneous Markov chains under a condition imposed to the maximal coefficient of correlation. The proofs are based on martingale techniques and a sharp lower…
When modelling metapopulation dynamics, the influence of a single patch on the metapopulation depends on the number of individuals in the patch. Since there is usually no obvious natural upper limit on the number of individuals in a patch,…
This paper establishes limit theorems for a class of stochastic hybrid systems (continuous deterministic dynamic coupled with jump Markov processes) in the fluid limit (small jumps at high frequency), thus extending known results for jump…
We establish self-norming central limit theorems for non-stationary time series arising as observations on sequential maps possessing an indifferent fixed point. These transformations are obtained by perturbing the slope in the…
In this paper, we study the asymptotic behavior of a supercritical $(\xi,\psi)$-superprocess $(X_t)_{t\geq 0}$ whose underlying spatial motion $\xi$ is an Ornstein-Uhlenbeck process on $\mathbb R^d$ with generator $L =…
We present normal approximation results at the process level for local functionals defined on dynamic Poisson processes in $\mathbb{R}^d$. The dynamics we study here are those of a Markov birth-death process. We prove functional limit…
We consider asymptotic behavior of Fourier transforms of stationary ergodic sequences with finite second moments. We establish a central limit theorem (CLT) for almost all frequencies and also an annealed CLT. The theorems hold for all…
Consider a branching Markov process, $X = (X(t), t \ge 0)$, with non-local branching mechanism. Studying the asymptotic behaviour of the moments of X has recently received attention in the literature [6, 7] due to the importance of these…
The main result of this paper is a functional limit theorem for the sine-process. In particular, we study the limit distribution, in the space of trajectories, for the number of particles in a growing interval. The sine-process has the…
Suppose that $X=(X_{t})_{t\ge 0}$ is either a general supercritical non-local branching Markov process, or a general supercritical non-local superprocess, on a Luzin space. Here, by ``supercritical" we mean that the mean semigroup of $X$…
A new sufficient condition is proposed in the problem of Central Limit Theorem in the array scheme for non-homogeneous Markov Chains.
This article presents a weak law of large numbers and a central limit theorem for the scaled realised covariation of a bivariate Brownian semistationary process. The novelty of our results lies in the fact that we derive the suitable…
We establish limit theorems for re-scaled occupation time fluctuations of a sequence of branching particle systems in $\R^d$ with anisotropic space motion and weakly degenerate splitting ability. In the case of large dimensions, our limit…
Our aim is to unify and extend the large deviation upper and lower bounds for the occupation times of a Markov process with $L_2$ semigroups under minimal conditions on the state space and the process trajectories; for example, no strong…
The production of molecules in a chemical reaction network is modelled as a Poisson process with a Markov-modulated arrival rate and an exponential decay rate. We analyze the distributional properties of $M$, the number of molecules, under…
In this paper, we consider a continuous-time Markov process and prove a local limit theorem for the integral of a time-inhomogeneous function of the process. One application is in the study of the fast-oscillating perturbations of linear…