Related papers: Piterbarg Theorems for Chi-processes with Trend

In this paper, we consider semi-Markov processes whose transition times and transition probabilities depend on a small parameter $\varepsilon$. Understanding the asymptotic behavior of such processes is needed in order to study the…

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 consider an Ornstein-Uhleneck (OU) process associated to self-normalised sums in i.i.d. symmetric random variables from the domain of attraction of $N(0, 1)$ distribution. We proved the self-normalised sums converge to the OU process (in…

This paper gives a new representation of Pickands' constants, which arise in the study of extremes for a variety of Gaussian processes. Using this representation, we resolve the long-standing problem of devising a reliable algorithm for…

We consider two independent Goldstein-Kac telegraph processes $X_1(t)$ and $X_2(t)$ on the real line $\Bbb R$, both developing with finite constant speed $c>0$, that, at the initial time instant $t=0$, simultaneously start from the origin…

The process $(G_t)_{t\in[0,T]}$ is referred to as a fractional Gaussian process if the first-order partial derivative of the difference between its covariance function and that of the fractional Brownian motion $(B^H_t)_{t\in[0,T ]}$ is a…

We build on recent works on Stein's method for functions of multivariate normal random variables to derive bounds for the rate of convergence of some asymptotically chi-square distributed statistics. We obtain some general bounds and…

This contribution investigates asymptotic properties of transient queue length process $$ Q(t)=\max\left(x+X(t)-ct, \sup_{0\leq s\leq t}\left(X(t)-X(s)-c(t-s)\right)\right),\ \ \ t\geq 0 $$ in Gaussian fluid queueing model, where input…

We consider a positive stationary generalized Ornstein--Uhlenbeck process \[V_t=\mathrm{e}^{-\xi_t}\biggl(\int_0^t\mathrm{e}^{\xi_{s-}}\ ,\mathrm{d}\eta_s+V_0\biggr)\qquadfor t\geq0,\] and the increments of the integrated generalized…

This paper introduces a quasi-likelihood ratio testing procedure for diffusion processes observed under nonsynchronous sampling schemes. High-frequency data, particularly in financial econometrics, are often recorded at irregular time…

In this paper, we study the asymptotic behavior, as the time $t$ goes to zero, of the trace of the semigroup of a killed relativistic $\alpha$-stable process in bounded $C^{1,1}$ open sets and bounded Lipschitz open sets. More precisely, we…

In this paper we derive Piterbarg's max-discretisation theorem for two different grids considering centered stationary vector Gaussian processes. So far in the literature results in this direction have been derived for the joint…

Let $X=\{X_n: n\in\mathbb{N}\}$ be a long memory linear process in which the coefficients are regularly varying and innovations are independent and identically distributed and belong to the domain of attraction of an $\alpha$-stable law…

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…

In many contexts such as queuing theory, spatial statistics, geostatistics and meteorology, data are observed at irregular spatial positions. One model of this situation involves considering the observation points as generated by a Poisson…

We consider a differential model describing nonisothermal fast phase separation processes taking place in a three-dimensional bounded domain. This model consists of a viscous Cahn-Hilliard equation characterized by the presence of an…

We consider the Pickands process {equation*} P_{n}(s)=\log (1/s)^{-1}\log \frac{X_{n-k+1,n}-X_{n-[k/s]+1,n}}{% X_{n-[k/s]+1,n}-X_{n-[k/s^{2}]+1,n}}, {equation*} {equation*} (\frac{k}{n}\leq s^2 \leq 1), {equation*} which is a generalization…

We study the extreme point process associated to the off-diagonal components in the matrix representation of the Gaussian $\beta$-Ensemble and prove its convergence to Poisson point process as $n\to +\infty$ when the inverse temperature…

This paper considers the effect of least squares procedures for nearly unstable linear time series with strongly dependent innovations. Under a general framework and appropriate scaling, it is shown that ordinary least squares procedures…

Let $A_t=\sum_{s\le t} F(X_{s-},X_s)$ be a purely discontinuous additive functional of a subordinate Brownian motion $X=(X_t, \mathbb P_x)$. We give a sufficient condition on the non-negative function $F$ that guarantees that finiteness of…