Related papers: Stationary max-stable fields associated to negativ…

For each $n\geq 1$, let $ {X_{in}, \quad i \geq 1} $ be independent copies of a nonnegative continuous stochastic process $X_{n}=(X_n(t))_{t\in T}$ indexed by a compact metric space $T$. We are interested in the process of partial maxima…

For $\{X(t), t \in G_\delta\}$ a centered Gaussian process with stationary increments and a.s. sample paths on a discrete grid $G_\delta=\{0,\delta,2\delta, ...\}$, where $\delta>0$, we investigate the stationary reflected process…

Max-stable processes are natural models for spatial extremes because they provide suitable asymptotic approximations to the distribution of maxima of random fields. In the recent past, several parametric families of stationary max-stable…

Consider a time-varying collection of n points on the positive real axis, modeled as exponentials of n Brownian motions whose drift vector at every time point is determined by the relative ranks of the coordinate processes at that time. If…

Let $\{X(t):t\in\mathbb R_+\}$ be a stationary Gaussian process with almost surely (a.s.) continuous sample paths, $\mathbb E X(t) = 0$, $\mathbb E X^2(t) = 1$ and correlation function satisfying (i) $r(t) = 1 - C|t|^{\alpha} +…

Let $\{X_i,i=1,2,...\}$ be i.i.d. standard gaussian variables. Let $S_n=X_1+...+X_n$ be the sequence of partial sums and $$ L_n=\max_{0\leq i<j\leq n}\frac{S_j-S_i}{\sqrt{j-i}}. $$ We show that the distribution of $L_n$, appropriately…

We consider the discrete Gaussian Free Field in a square box in $\mathbb Z^2$ of side length $N$ with zero boundary conditions and study the joint law of its properly-centered extreme values ($h$) and their scaled spatial positions ($x$) in…

In a bounded domain $\mathcal{O}\subset\mathbb{R}^3$ of class $C^{1,1}$, we consider a stationary Maxwell system with the perfect conductivity boundary conditions. It is assumed that the dielectric permittivity and the magnetic permeability…

We consider a class of stochastic processes $X$ defined by $X\left( t\right) =\int_{0}^{T}G\left( t,s\right) dM\left( s\right) $ for $t\in\lbrack0,T]$, where $M$ is a square-integrable continuous martingale and $G$ is a deterministic…

Let $\{Z(\tau,s), (\tau,s)\in [a,b]\times[0,T]\}$ with some positive constants $a,b,T$ be a centered Gaussian random field with variance function $\sigma^{2}(\tau,s)$ satisfying $\sigma^{2}(\tau,s)=\sigma^{2}(\tau)$. We firstly derive the…

Max-stable processes provide natural models for the modelling of spatial extreme values observed at a set of spatial sites. Full likelihood inference for max-stable data is, however, complicated by the form of the likelihood function as it…

We are interested in estimating the location of what we call "smooth change-point" from $n$ independent observations of an inhomogeneous Poisson process. The smooth change-point is a transition of the intensity function of the process from…

The paper investigates uniform convergence of wavelet expansions of Gaussian random processes. The convergence is obtained under simple general conditions on processes and wavelets which can be easily verified. Applications of the developed…

Given a Gibbs point process $\P^{\Psi}$ on $\R^d$ having a weak enough potential $\Psi$, we consider the random measures $\mu_\la := \sum_{x \in \P^{\Psi} \cap Q_\la} \xi(x, \P^{\Psi} \cap Q_\la) \delta_{x/\la^{1/d}}$, where $Q_{\la} :=…

We consider a model of Branching Brownian Motion with time-inhomogeneous variance of the form \sigma(t/T), where \sigma is a strictly decreasing function. Fang and Zeitouni (2012) showed that the maximal particle's position M_T is such that…

Assume that a stochastic processes can be approximated, when some scale parameter gets large, by a fluid limit (also called "mean field limit", or "hydrodynamic limit"). A common practice, often called the "fixed point approximation"…

We provide a sufficient condition for the bounded law of the iterated logarithms for strictly stationary random fields expressable as a functional of i.i.d. random fields when the summation is done on rectangles. The study is done via the…

We revisit the convergence analysis of constant stepsize stochastic approximation (SA) with decision-dependent Markovian noise, with a focus on characterizing the stationary bias against the root of the mean-field equation. We first…

Let $W_t$ be a standard Brownian motion. It is well-known that the Langevin equation $d U_t = -\theta U_td t + d W_t$ defines a stationary process called Ornstein-Uhlenbeck process. Furthermore, Langevin equation can be used to construct…

In a classical problem for the stopping of a diffusion process $(X_t)_{t \geq 0}$, where the goal is to maximise the expected discounted value of a function of the stopped process ${\mathbb E}^x[e^{-\beta \tau}g(X_\tau)]$, maximisation…