Related papers: Profile cut-off phenomenon for the ergodic Feller …

We introduce a new framework for analyzing (Quasi-}Newton type methods applied to non-smooth optimization problems. The source of randomness comes from the evaluation of the (approximation) of the Hessian. We derive, using a variant of…

This work is devoted to the study of conservative affine processes on the canonical state space $D = $R_+^m \times \R^n$, where $m + n > 0$. We show that each affine process can be obtained as the pathwise unique strong solution to a…

We investigate the problem of the rate of convergence to equilibrium for ergodic stochastic differential equations driven by fractional Brownian motion with Hurst parameter $H\in (1/3,1)$ and multiplicative noise component $\sigma$. When…

The cutoff phenomenon is an abrupt transition from out of equilibrium to equilibrium undergone by certain Markov processes in the limit where the size of the state space tends to infinity: instead of decaying gradually over time, their…

This note proves that the separation convergence towards the uniform distribution abruptly occurs at times around ln(n)/n for the (time-accelerated by 2) Brownian motion on the sphere with a high dimension n. The arguments are based on a…

We obtain strong consistency and asymptotic normality of a least squares estimator of the drift coefficient for complex-valued Ornstein-Uhlenbeck processes disturbed by fractional noise, extending the result of Y. Hu and D. Nualart,…

We study convergence to equilibrium for a large class of Markov chains in random environment. The chains are sparse in the sense that in every row of the transition matrix $P$ the mass is essentially concentrated on few entries. Moreover,…

In this paper we prove the following result, useful and often needed in the study of the ergodic properties of hard ball systems: In any such system, for any phase point x with a non-singular forward trajectory and infinitely many connected…

Let $f:\mathbb{R} \to \mathbb{R}$ be a stationary centered Gaussian process. For any $R>0$, let $\nu_R$ denote the counting measure of $\{x \in \mathbb{R} \mid f(Rx)=0\}$. In this paper, we study the large $R$ asymptotic distribution of…

We study statistical inference of the drift parameters for the Volterra Ornstein-Uhlenbeck process on R in the ergodic regime. For continuous-time observations, we derive the corresponding maximum likelihood estimators and show that they…

We develop a theory of ergodicity for a class of random dynamical systems where the driving noise is not white. The two main tools of our analysis are the strong Feller property and topological irreducibility, introduced in this work for a…

A perturbative quantum theory of the 2-Killing vector reduction of general relativity is constructed. Although non-renormalizable in the standard sense, we show that to all orders of the loop expansion strict cut-off independence can be…

We provide non-asymptotic error bounds in the path Wasserstein distance with quadratic integral cost between suitable functionals of the telegraph process and the corresponding functional of Brownian motion with explicit diffusivity…

Recent extensive numerical experiments in high scale machine learning have allowed to uncover a quite counterintuitive phase transition, as a function of the ratio between the sample size and the number of parameters in the model. As the…

In the framework of a real Hilbert space, we address the problem of finding the zeros of the sum of a maximally monotone operator $A$ and a cocoercive operator $B$. We study the asymptotic behaviour of the trajectories generated by a second…

We study the problem of minimizing a relatively-smooth convex function using stochastic Bregman gradient methods. We first prove the convergence of Bregman Stochastic Gradient Descent (BSGD) to a region that depends on the noise (magnitude…

We study a non-reversible random walk advected by the symmetric simple exclusion process, so that the walk has a local drift of opposite sign when sitting atop an occupied or an empty site. We prove that the back-tracking probability of the…

Given a family of rotationally symmetric compact manifolds indexed by the dimension and a weight function, the goal of this paper is to investigate the cut-off phenomenon for the Brownian motions on this family. We provide a class of…

Let $L\geq0$ and $0<\varepsilon\ll1$. Consider the following time-dependent family of $1D$ Schr\"{o}dinger equations with scaled and translated harmonic oscillator potentials $ i\varepsilon\partial_t…

We refer by threshold Ornstein-Uhlenbeck to a continuous-time threshold autoregressive process. It follows the Ornstein-Uhlenbeck dynamics when above or below a fixed level, yet at this level (threshold) its coefficients can be…