Related papers: Limit theorems for $p$-domain functionals of stati…

Max-stable random fields are very appropriate for the statistical modelling of spatial extremes. Hence, integrals of functions of max-stable random fields over a given region can play a key role in the assessment of the risk of natural…

A non-classical formulation of the central limit theorem is given for sequences of independent random variables with finite second moments. Singular sequences whose members all have a degenerate or normal distribution are excluded from…

We study a Gibbs measure over Brownian motion with a pair potential which depends only on the increments. Assuming a particular form of this pair potential, we establish that in the infinite volume limit the Gibbs measure can be viewed as…

We provide new limit theory for functionals of a general class of processes lying at the boundary between stationarity and nonstationarity -- what we term weakly nonstationary processes (WNPs). This includes, as leading examples, fractional…

Let $\nu\in M^1([0,\infty[)$ be a fixed probability measure. For each dimension $p\in \mathbb{N}$, let $(X_n^{p})_{n\geq1}$ be i.i.d. $\mathbb{R}^p$-valued random variables with radially symmetric distributions and radial distribution…

Let $\mathbb{B}_p^N$ be the $N$-dimensional unit ball corresponding to the $\ell_p$-norm. For each $N\in\mathbb N$ we sample a uniform random subspace $E_N$ of fixed dimension $m\in\mathbb{N}$ and consider the volume of $\mathbb{B}_p^N$…

Here I prove non-central limit theorems for non-linear functionals of vector valued stationary random fields under appropriate conditions. They are the multivariate versions of the results in paper\cite{2}. Previously A. M. Arcones…

The aim of this paper is investigating the existence of one or more critical points of a family of functionals which generalizes the model problem \[ \bar J(u)\ =\ \frac1p\ \int_\Omega \bar A(x,u)|\nabla u|^p dx - \int_\Omega G(x,u) dx \]…

We prove a Central Limit Theorem for the finite dimensional distributions of the displacement for the 1D self-repelling diffusion which solves \begin{equation*} dX_t =dB_t -\big(G'(X_t)+ \int_0^t F'(X_t-X_s)ds\big)dt, \end{equation*} where…

We prove a functional central limit theorem for subgraph counts in a dynamic version of the random connection model. To establish tightness, we develop a dynamic extension of the cumulant method.

We study the one-dimensional stochastic wave equation driven by a Gaussian multiplicative noise which is white in time and has the covariance of a fractional Brownian motion with Hurst parameter $H\in [1/2,1)$ in the spatial variable. We…

We consider a stationary sequence $(X_n)$ constructed by a multiple stochastic integral and an infinite-measure conservative dynamical system. The random measure defining the multiple integral is non-Gaussian, infinitely divisible and has a…

We study some sufficient conditions imposed on the sequence of martingale differences (m.d.) in the separable Banach spaces of continuous functions defined on the metric compact set for the Central Limit Theorem in this space. We taking…

We study the central limit theorem for sums of independent tensor powers, $\frac{1}{\sqrt{d}}\sum\limits_{i=1}^d X_i^{\otimes p}$. We focus on the high-dimensional regime where $X_i \in \mathbb{R}^n$ and $n$ may scale with $d$. Our main…

Many statistical applications require establishing central limit theorems for sums, integrals, or for quadratic forms of functions of a stationary process. A particularly important case is that of Appell polynomials, since the Appell…

For each open, bounded and convex domain $\Omega \subset \mathbb{R}^{D},$ $D\geq 2$, and each real number $p>1,$ we denote by $u_{p}$ the $p$\emph{-torsion function} on $\Omega $, i.e. the solution of the \emph{torsional creep problem}…

We construct $P(phi)_1$-processes indexed by the full time-line, separately derived from the functional integral representations of the relativistic and non-relativistic Nelson models in quantum field theory. These two cases differ…

We investigate branching processes in nearly degenerate varying environment, where the offspring distribution converges to the degenerate distribution at 1. Such processes die out almost surely, therefore, we condition on non-extinction or…

Given a set $T \subset (0, +\infty)$, intervals $I\subset (0, +\infty)$ and $J\subset {\mathbb R}$, as well as functions $g_t:I\times J\rightarrow J$ with $t$'s running through the set \[ T^{\ast}:=T \cup \big\{t^{-1}\colon t \in…

In this paper, we investigate the functional central limit theorem for stochastic processes associated to partial sums of additive functionals of reversible Markov chains with general spate space, under the normalization standard deviation…