Related papers: Quasi-Stationary Distributions for Stochastic Appr…
We establish sufficient conditions for exponential convergence to a unique quasi-stationary distribution in the total variation norm. These conditions also ensure the existence and exponential ergodicity of the Q-process, the process…
ODE solvers with randomly sampled timestep sizes appear in the context of chaotic dynamical systems, differential equations with low regularity, and, implicitly, in stochastic optimisation. In this work, we propose and study the stochastic…
This article studies the quasi-stationary behaviour of absorbed one-dimensional diffusions. We obtain necessary and sufficient conditions for the exponential convergence to a unique quasi-stationary distribution in total variation,…
In this paper we address the convergence of stochastic approximation when the functions to be minimized are not convex and nonsmooth. We show that the "mean-limit" approach to the convergence which leads, for smooth problems, to the ODE…
Quasistationary states are long-lived nonequilibrium states, observed in some systems with long-range interactions under deterministic Hamiltonian evolution. These intriguing non-Boltzmann states relax to equilibrium over times which…
A Quasi-Stationary Distribution (QSD)for a Markov process with an almost surely hit absorbing state is a time-invariant initial distribution for the process conditioned on not being absorbed by any given time. An initial distribution for…
Given a nonsmooth, nonconvex minimization problem, we consider algorithms that iteratively sample and minimize stochastic convex models of the objective function. Assuming that the one-sided approximation quality and the variation of the…
In this paper, an alternative approximation to the innovation method is introduced for the parameter estimation of diffusion processes from partial and noisy observations. This is based on a convergent approximation to the first two…
An algorithm of searching a zero of an unknown undimensional function is considered, measured at a point x with some error. The step sizes are random positive values and are calculated according to the rule: if two consecutive iterations…
We study the fundamental problem of high-dimensional mean estimation in a robust model where a constant fraction of the samples are adversarially corrupted. Recent work gave the first polynomial time algorithms for this problem with…
Motivated by the recent contribution \cite{BB17} we study the scaling limit behavior of a class of one-dimensional stochastic differential equations which has a unique attracting point subject to a small additional repulsive perturbation.…
We characterise all the quasi-stationary distributions and the Q-process associated with a continuous state branching process that explodes in finite time. We also provide a rescaling for the continuous state branching process conditioned…
We consider stochastic approximation with block-coordinate stepsizes and propose adaptive stepsize rules that aim to minimize the expected distance from the next iterate to an (unknown) target point. These stepsize rules employ online…
We study the almost sure convergence of the Stochastic Approximation algorithm to the fixed point $x^\star$ of a nonlinear operator under a negative drift condition and a general noise sequence with finite $p$-th moment for some $p > 1$.…
In sustained growth with random dynamics stationary distributions can exist without detailed balance. This suggests thermodynamical behavior in fast growing complex systems. In order to model such phenomena we apply both a discrete and a…
A finite point process is characterized by the distribution of the number of points (the size) of the process. In some applications, for example, in the context of packet flows in modern communication networks, it is of interest to infer…
We analyze a stochastic approximation algorithm for decision-dependent problems, wherein the data distribution used by the algorithm evolves along the iterate sequence. The primary examples of such problems appear in performative prediction…
For a large class of processes with an absorbing state, statistical properties of the surviving sample attain time-independent values in the quasi-stationary (QS) regime. We propose a practical simulation method for studying…
We consider the symmetric simple exclusion process on Z^d, for d>= 5, and study the regularity of the quasi-stationary measures of the dynamics conditionned on not occupying the origin. For each \rho\in ]0,1[, we establish uniqueness of the…
We provide a numerically robust and fast method capable of exploiting the local geometry when solving large-scale stochastic optimisation problems. Our key innovation is an auxiliary variable construction coupled with an inverse Hessian…