Related papers: High-frequency Estimation of the L\'evy-driven Gra…
We consider a nonlocal evolution equation representing the continuum limit of a large ensemble of interacting particles on graphs forced by noise. The two principle ingredients of the continuum model are a nonlocal term and Q-Wiener process…
We study the least squares estimator for the drift parameter of the Langevin stochastic equation driven by the Rosenblatt process. Using the techniques of the Malliavin calculus and the stochastic integration with respect to the Rosenblatt…
We present a new angle on the expressive power of graph neural networks (GNNs) by studying how the predictions of real-valued GNN classifiers, such as those classifying graphs probabilistically, evolve as we apply them on larger graphs…
We consider the rates of relaxation of a particle in a harmonic well, subject to L\'evy noise characterized by its L\'evy index $\mu$. Using the propagator for this L\'evy Ornstein-Uhlenbeck process (LOUP), we show that the eigenvalue…
In this paper, we study nonparametric estimation of the L\'{e}vy density for L\'{e}vy processes, with and without Brownian component. For this, we consider $n$ discrete time observations with step $\Delta$. The asymptotic framework is: $n$…
We develop here a stochastic framework for modeling and segmenting transient spindle-like oscillatory bursts in electroencephalogram (EEG) signals. At the modeling level, individual spindles are represented as path realizations of a…
Stochastic burst-like oscillations are common in physiological signals, yet there are few compact generative models that capture their transient structure. We propose a numerical-twin framework that represents transient narrowband activity…
Among all generalized Ornstein-Uhlenbeck processes which sample the same invariant measure and for which the same amount of randomness (a $N$-dimensional Brownian motion) is injected in the system, we prove that the asymptotic rate of…
Large graphs are sometimes studied through their degree sequences (power law or regular graphs). We study graphs that are uniformly chosen with a given degree sequence. Under mild conditions, it is shown that sequences of such graphs have…
We study the application of graph random features (GRFs) - a recently introduced stochastic estimator of graph node kernels - to scalable Gaussian processes on discrete input spaces. We prove that (under mild assumptions) Bayesian inference…
We investigate the asymptotic behavior of the maximum likelihood estimators of the unknown parameters of positive recurrent Ornstein-Uhlenbeck processes driven by Ornstein-Uhlenbeck processes.
We develop a new model selection method for the adaptive robust efficient nonparametric signal estimation observed with impulse noise which is defined by the general non Gaussian L\'evy processes. On the basis of the developed method, we…
In this work, we investigate a range of time series, including Gaussian noises (white, pink, and blue), stochastic processes (Ornstein-Uhlenbeck, fractional Brownian motion, and Levy flights), and chaotic systems (the logistic map), using…
The Ornstein-Uhlenbeck (OU) process describes the dynamics of Brownian particles in a confining harmonic potential, thereby constituting the paradigmatic model of overdamped, mean-reverting Langevin dynamics. Despite its widespread…
We study the strong approximation of a rough volatility model, in which the log-volatility is given by a fractional Ornstein-Uhlenbeck process with Hurst parameter $H<1/2$. Our methods are based on an equidistant discretization of the…
Stochastic Gradient Descent (SGD) is an important algorithm in machine learning. With constant learning rates, it is a stochastic process that, after an initial phase of convergence, generates samples from a stationary distribution. We show…
This article establishes cutoff stability also known as abrupt thermalization for generic multidimensional Hurwitz stable Ornstein-Uhlenbeck systems with (possibly degenerate) L\'evy noise at fixed noise intensity. The results are based on…
Functional data present as functions or curves possessing a spatial or temporal component. These components by nature have a fixed observational domain. Consequently, any asymptotic investigation requires modelling the increased correlation…
We consider Ornstein-Uhlenbeck processes (OU-processes) associated to hypoelliptic diffusion processes on finite-dimensional Lie groups: let $ \mathcal{L} $ be a hypoelliptic, left-invariant ``sum of the squares''-operator on a Lie group $…
The goal of this paper is to construct ergodic estimators for the parameters in the double exponential Ornstein-Uhlenbeck process, observed at discrete time instants with time step size h. The existence and uniqueness, the strong…