Related papers: Asymptotic properties of U-processes under long-ra…

Consider a sequence of Poisson random connection models (X_n,lambda_n,g_n) on R^d, where lambda_n / n^d \to lambda > 0 and g_n(x) = g(nx) for some non-increasing, integrable connection function g. Let I_n(g) be the number of isolated…

Let $U_h:\mathbb R^{d}\to \mathbb R^{d}$ be a smooth vector field and consider the associated overdamped Langevin equation $$dX_t=-U_h(X_t)\,dt+\sqrt{2h}\,dB_t$$ in the low temperature regime $h\rightarrow 0$. In this work, we study the…

We study the continuous-time version of the empirical correlation coefficient between the paths of two possibly correlated Ornstein-Uhlenbeck processes, known as Yule's nonsense correlation for these paths. Using sharp tools from the…

Fix an integer k, and let I(l), l=1,2,..., be a sequence of k-dimensional vectors of multiple Wiener-It\^o integrals with respect to a general Gaussian process. We establish necessary and sufficient conditions to have that, as l diverges,…

Let $P$ be a simple,stationary point process having fast decay of correlations, i.e., its correlation functions factorize up to an additive error decaying faster than any power of the separation distance. Let $P_n:= P \cap W_n$ be its…

For each $N\geq 1$, let $G_N$ be a simple random graph on the set of vertices $[N]=\{1,2, ..., N\}$, which is invariant by relabeling of the vertices. The asymptotic behavior as $N$ goes to infinity of correlation functions: $$ \mathfrak…

Special case of a Gibbsian facet process on a fixed window with a discrete orientation distribution and with increasing intensity of the underlying Poisson process is studied. All asymptotic moments for interaction U-statistics are…

Let $\{X(t),t\ge0\}$ be a centered Gaussian process and let $\gamma$ be a non-negative constant. In this paper we study the asymptotics of $P\{\underset{t\in [0,\mathcal{T}/u^\gamma]}\sup X(t)>u\}$ as $u\to\infty$, with $\mathcal{T}$ an…

We consider non-ergodic class of stationary real harmonizable symmetric $\alpha$-stable processes $X=\left\{X(t):t\in\mathbb{R}\right\}$ with a finite symmetric and absolutely continuous control measure. We refer to its density function as…

Let $(X_{k})_{k \in \mathbb Z }$ be a linear process with values in a separable Hilbert space $\mathbb{H}$ given by $X_{k} =\sum_{j=0}^{\infty} (j+1)^{-N}\varepsilon_{k-j}$ for each $k \in \mathbb Z$, where $N:\mathbb{H} \to \mathbb{H}$ is…

We consider a general class of statistical experiments, in which an $n$-dimensional centered Gaussian random variable is observed and its covariance matrix is the parameter of interest. The covariance matrix is assumed to be…

We derive, up to a constant factor, matching lower and upper bounds on the concentration functions of suprema of separable centered Gaussian processes and order statistics of Gaussian random fields. These bounds reveal that suprema of…

This paper studies the asymptotic properties of weighted sums of the form $Z_n=\sum_{i=1}^n a_i X_i$, in which $X_1, X_2, \ldots, X_n$ are i.i.d.~random variables and $a_1, a_2, \ldots, a_n$ correspond to either eigenvalues or singular…

The article is devoted to the nonparametric estimation of the quadratic covariation of non-synchronously observed It\^o processes in an additive microstructure noise model. In a high-frequency setting, we aim at establishing an asymptotic…

A joint limit theorem for the point process of the off-diagonal entries of a sample covariance matrix $\mathbf{S}$, constructed from $n$ observations of a $p$-dimensional random vector with iid components, and the Frobenius norm of…

We derive exact tail asymptotics of sojourn time above the level $u\geq 0$ $$ \mathbb{P}\left(v(u)\int_0^T \mathbb{I}(X(t)-ct>u)d t>x\right), \quad x\geq 0 $$ as $u\to\infty$, where $X$ is a Gaussian process with continuous sample paths,…

In this paper, we study the distribution of the so-called "Yule's nonsense correlation statistic" on a time interval $[0,T]$ for a time horizon $T>0$ , when $T$ is large, for a pair $(X_{1},X_{2})$ of independent Ornstein-Uhlenbeck…

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…

We consider $U$-statistics on row-column exchangeable matrices, arrays invariant to separate permutations of rows and columns and common in bipartite data. Under the standard dissociation assumption, we develop a graph-indexed analogue of…

Let $\chi_n(t) = (\sum_{i=1}^n X_i^2(t))^{1/2},t\ge0$ be a chi-process with $n$ degrees of freedom where $X_i$'s are independent copies of some generic centered Gaussian process $X$. This paper derives the exact asymptotic behavior of…