Related papers: Persistence probabilities in centered, stationary,…
The predictability of discrete-time processes is studied in a deterministic setting. A family of one-step-ahead predictors is suggested for processes of which the energy decays at higher frequencies. For such processes, the prediction error…
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…
Gaussian process (GP) models are widely used to emulate propagation uncertainty in computer experiments. GP emulation sits comfortably within an analytically tractable Bayesian framework. Apart from propagating uncertainty of the input…
The article contains an overview over locally stationary processes. At the beginning time varying autoregressive processes are discussed in detail - both as as a deep example and an important class of locally stationary processes. In the…
We investigate the limiting behavior of discrete determinantal point processes (DPPs) towards continuous DPPs when the size of the set to sample from goes to infinity. We propose a non-asymptotic characterization of this limit in terms of…
Simulations of a stochastic fixed-energy sandpile in one and two dimensions reveal slow relaxation of the order parameter, even far from the critical point. The decay of the activity is best described by a stretched-exponential form. The…
For AR(1)-processes $X_n=\rho X_{n-1}+\xi_n$, $n\in\mathbb{N}$, where $\rho\in\mathbb{R}$ and $(\xi_i)_{i\in\mathbb{N}}$ is an i.i.d. sequence of random variables, we study the persistence probabilities $\mathbb{P}(X_0\ge 0,\dots, X_N\ge…
We analyze the performance of quantum parameter estimation in the presence of the most general Gaussian dissipative reservoir. We derive lower bounds on the precision of phase estimation and a closely related problem of frequency…
The randomized Gauss--Seidel method and its extension have attracted much attention recently and their convergence rates have been considered extensively. However, the convergence rates are usually determined by upper bounds, which cannot…
We consider the 1D Expected Improvement optimization based on Gaussian processes having spectral densities converging to zero faster than exponentially. We give examples of problems where the optimization trajectory is not dense in the…
The problem of a diffusing particle moving among diffusing traps is analyzed in general space dimension d. We consider the case where the traps are initially randomly distributed in space, with uniform density rho, and derive upper and…
This paper concerns the instantaneous frequency (IF) of continuous-time, zero-mean, complex-valued, proper, mean-square differentiable nonstationary Gaussian stochastic processes. We compute the probability density function for the IF for…
We study persistence probabilities of Hermite processes. As a tool, we derive a general decorrelation inequality for the Rosenblatt process, which is reminiscent of Slepian's lemma for Gaussian processes or the FKG inequality and which may…
First, we present some results about the H\"older continuity of the sample paths of so called dilatively stable processes which are certain infinitely divisible processes having a more general scaling property than self-similarity. As a…
This note is concerned with weakly interacting stochastic particle systems with possibly singular pairwise interactions. In this setting, we observe a connection between entropic propagation of chaos and exponential concentration bounds for…
Multistable processes, that is, processes which are, at each "time", tangent to a stable process, but where the index of stability varies along the path, have been recently introduced as models for phenomena where the intensity of jumps is…
A time-varying empirical spectral process indexed by classes of functions is defined for locally stationary time series. We derive weak convergence in a function space, and prove a maximal exponential inequality and a…
Consider a discrete-time martingale $\{X_t\}$ taking values in a Hilbert space $\mathcal H$. We show that if for some $L \geq 1$, the bounds $\mathbb{E} \left[\|X_{t+1}-X_t\|_{\mathcal H}^2 \mid X_t\right]=1$ and $\|X_{t+1}-X_t\|_{\mathcal…
Discrete stability extends the classical notion of stability to random elements in discrete spaces by defining a scaling operation in a randomised way: an integer is transformed into the corresponding binomial distribution. Similarly…
In this work, we consider a binary sequential hypothesis testing problem with distributed and asynchronous measurements. The aim is to analyze the effect of sampling times of jointly $\textit{wide-sense stationary}$ (WSS) Gaussian…