Related papers: A spectral approach for quenched limit theorems fo…
Suppose $B_i:= B(p,r_i)$ are nested balls of radius $r_i$ about a point $p$ in a dynamical system $(T,X,\mu)$. The question of whether $T^i x\in B_i$ infinitely often (i. o.) for $\mu$ a.e.\ $x$ is often called the shrinking target problem.…
Statistical inferences for sample correlation matrices are important in high dimensional data analysis. Motivated by this, this paper establishes a new central limit theorem (CLT) for a linear spectral statistic (LSS) of high dimensional…
We obtain pointwise ergodic theorems with rate under conditions expressed in terms of the convergence of series involving $\|\sum_{k=1} ^nf\circ \theta^k\|_2$, improving previous results. Then, using known results on martingale…
Under a Lipschitz condition on distribution dependent coefficients, the central limit theorem and the moderate deviation principle are obtained for solutions of McKean-Vlasov type stochastic differential equations, which extend from the…
In this paper we establish spatial central limit theorems for a large class of supercritical branching Markov processes with general spatial-dependent branching mechanisms. These are generalizations of the spatial central limit theorems…
Let $p\in[1,\infty]$. Consider the projection of a uniform random vector from a suitably normalized $\ell^p$ ball in $\mathbb{R}^n$ onto an independent random vector from the unit sphere. We show that sequences of such random projections,…
In this paper we will prove various probabilistic limit theorems for some classes of distance expanding sequential dynamical systems (SDS). Our starting point here is certain sequential complex Ruelle-Perron-Frobenius (RPF) theorems which…
We study the relationship between chaotic behavior and the Central Limit Theorem (CLT) in the Kuramoto model. We calculate sums of angles at equidistant times along deterministic trajectories of single oscillators and we show that, when…
We prove a limit theorem for quantum stochastic differential equations with unbounded coefficients which extends the Trotter-Kato theorem for contraction semigroups. From this theorem, general results on the convergence of approximations…
Through certain appropriate constructions, we establish periodic solutions in distribution for some stochastic differential equations with infinite-dimensional Levy noise. Additionally, we obtain the corresponding periodic measures and…
The law of large numbers (LLN) and central limit theorem (CLT) are long and widely been known as two fundamental results in probability theory. Recently problems of model uncertainties in statistics, measures of risk and superhedging in…
The work [8] established memory loss in the time-dependent (non-random) case of uniformly expanding maps of the interval. Here we find conditions under which we have convergence to the normal distribution of the appropriately scaled…
Consider the partial sums {S_t} of a real-valued functional F(Phi(t)) of a Markov chain {Phi(t)} with values in a general state space. Assuming only that the Markov chain is geometrically ergodic and that the functional F is bounded, the…
We present a molecular dynamics test of the Central Limit Theorem (CLT) in a paradigmatic long-range-interacting many-body classical Hamiltonian system, the HMF model. We calculate sums of velocities at equidistant times along deterministic…
We consider N single server infinite buffer queues with service rate \beta. Customers arrive at rate N\alpha, choose L queues uniformly, and join the shortest. We study the processes R^N for large N, where R^N_t(k) is the fraction of queues…
Statistical inference for non-stationary data is hindered by the failure of classical central limit theorems (CLTs), not least because there is no fixed Gaussian limit to converge to. To resolve this, we introduce relative weak convergence,…
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…
For sequences of non-lattice weakly dependent random variables, we obtain asymptotic expansions for Large Deviation Principles. These expansions, commonly referred to as strong large deviation results, are in the spirit of Edgeworth…
We consider the Fleming--Viot particle system associated with a continuous-time Markov chain in a finite space. Assuming irreducibility, it is known that the particle system possesses a unique stationary distribution, under which its…
The main objective of this article is to establish a central limit theorem for additive three-variable functionals of bifurcating Markov chains. We thus extend the central limit theorem under point-wise ergodic conditions studied in…