Related papers: On Sampling of stationary increment processes
Sampling the stationary points of a complicated potential energy landscape is a challenging problem. Here we introduce a sampling method based on relaxation from stationary points of the highest index of the Hessian matrix. We illustrate…
Regularly varying stochastic processes model extreme dependence between process values at different locations and/or time points. For such processes we propose a two-step parameter estimation of the extremogram, when some part of the domain…
Consider a process, stochastic or deterministic, obtained by using a numerical integration scheme, or from Monte-Carlo methods involving an approximation to an integral, or a Newton-Raphson iteration to approximate the root of an equation.…
Max-stable processes are widely used to model spatial extremes. These processes exhibit asymptotic dependence meaning that the large values of the process can occur simultaneously over space. Recently, inverted max-stable processes have…
In this article, we primarily propose a novel Bayesian characterization of stationary and nonstationary stochastic processes. In practice, this theory aims to distinguish between global stationarity and nonstationarity for both parametric…
Maximum likelihood estimations for the parameters of extreme value distributions are discussed in this paper using fixed point iteration. The commonly used numerical approach for addressing this problem is the Newton-Raphson approach which…
Motivated by the construction of the It\^o stochastic integral, we consider a step function method to discretize and simulate volatility modulated L\'evy semistationary processes. Moreover, we assess the accuracy of the method with a…
The zero range process is of particular importance as a generic model for domain wall dynamics of one-dimensional systems far from equilibrium. We study this process in one dimension with rates which induce an effective attraction between…
We obtain an almost sure bound for oscillation rates of empirical distribution functions for stationary causal processes. For short-range dependent processes, the oscillation rate is shown to be optimal in the sense that it is as sharp as…
In this short note we will provide a sufficient and necessary condition to have uniqueness of the location of the maximum of a stochastic process over an interval. The result will also express the mean value of the location in terms of the…
Assuming a $q$-variant of the prime $k$-tuple conjecture uniformly, we compute mixed moments of the number of primes in disjoint short intervals and progressions, respectively. This involves estimating the mean of singular series along…
In this paper we consider the problem of estimating the parameters of a Poisson arrival process where the rate function is assumed to lie in the span of a known basis. Our goal is to estimate the basis expansions coefficients given a…
We study the probability of a real-valued stationary process to be positive on a large interval $[0,N]$. We show that if in some neighborhood of the origin the spectral measure of the process has density which is bounded away from zero and…
Let $\mathbf{X}=\{X_{n}\}_{n\geq 1}$ be a sequence of stationary Gaussian variables and suppose that only some of the random variables from $\mathbf{X}$ can be observed. In this paper, by studying the limiting properties of multidimensional…
We consider a stationary queueing process $Q_X$ fed by a centered Gaussian process $X$ with stationary increments and variance function satisfying classical regularity conditions. A criterion when, for a given function $f$, $\mathbb P…
An algorithm for the unbiased simulation of continuous max-(resp.\ min-)id stochastic processes is developed. The algorithm only requires the simulation of finite Poisson random measures on the space of continuous functions and avoids the…
We consider a stationary random field indexed by an increasing sequence of subsets of $\mathbb{Z}^d$ obeying a very broad geometrical assumption on how the sequence expands. Under certain mixing and local conditions, we show how the tail…
This contribution aims at studying the behaviour of the classical sample moment estimator, $S(n,q)= \sum_{k=1}^n X_k^{q}/n $, as a function of the number of available samples $n$, in the case where the random variables $X$ are positive,…
The exact statistics of an arbitrary quantum observable is analytically obtained. Due to the probabilistic nature of a sequence of intermediate measurements and stochastic fluctuations induced by the interaction with the environment, the…
Random processes with stationary increments and intrinsic random processes are two concepts commonly used to deal with non-stationary random processes. They are broader classes than stationary random processes and conceptually closely…