Related papers: On optimal stationary couplings between stationary…
The zig-zag process is a piecewise deterministic Markov process in position and velocity space. The process can be designed to have an arbitrary Gibbs type marginal probability density for its position coordinate, which makes it suitable…
For quantum systems with linear dynamics in phase space much of classical feedback control theory applies. However, there are some questions that are sensible only for the quantum case, such as: given a fixed interaction between the system…
We present new Poisson process approximation results for stabilizing functionals of Poisson and binomial point processes. These functionals are allowed to have an unbounded range of interaction and encompass many examples in stochastic…
In this work, we provide faster algorithms for approximating the optimal transport distance, e.g. earth mover's distance, between two discrete probability distributions $\mu, \nu \in \Delta^n$. Given a cost function $C : [n] \times [n] \to…
We consider the stability of Robust Optimization problems with respect to perturbations in their uncertainty sets. We focus on Linear Optimization problems, including those with a possibly infinite number of constraints, also known as…
This article connects the theory of extremal doubly stochastic measures to the geometry and topology of optimal transportation. We begin by reviewing an old question (# 111) of Birkhoff in probability and statistics [4], which is to give a…
We consider the limit distribution of maxima of periodograms for stationary processes. Our method is based on $m$-dependent approximation for stationary processes and a moderate deviation result.
A new pairwise cost function is proposed for the optimal transport barycenter problem, adopting the form of the minimal action between two points, with a Lagrangian that takes into account an underlying probability distribution. Under this…
We provide explicit formulaes for the first Kantorovich-Wasserstein distance between stationary measures for iterated function scheme on the unit interval. In particular, we consider two stationary measures with different configurations of…
We introduce a new class of stochastic processes which are stationary, Markovian and characterized by an infinite range of time-scales. By transforming the Fokker-Planck equation of the process into a Schrodinger equation with an…
This paper is concerned with the development of rigorous approximations to various expectations associated with Markov chains and processes having non-stationary transition probabilities. Such non-stationary models arise naturally in…
We develop an approach for solving one-sided optimal stopping problems in discrete time for general underlying Markov processes on the real line. The main idea is to transform the problem into an auxiliary problem for the ladder height…
The phenomenon of mutual coupling in continuous aperture arrays (CAPAs) is studied. First, a general physical model for the phenomenon that accounts for both polarization and surface dissipation losses is developed. Then, the unipolarized…
We observe a length-$n$ sample generated by an unknown,stationary ergodic Markov process (\emph{model}) over a finite alphabet $\mathcal{A}$. Given any string $\bf{w}$ of symbols from $\mathcal{A}$ we want estimates of the conditional…
We prove explicit error bounds for Markov chain Monte Carlo (MCMC) methods to compute expectations of functions with unbounded stationary variance. We assume that there is a $p\in(1,2)$ so that the functions have finite $L_p$-norm. For…
We survey existing techniques to bound the mixing time of Markov chains. The mixing time is related to a geometric parameter called conductance which is a measure of edge-expansion. Bounds on conductance are typically obtained by a…
We obtain a sharp convergence rate for banded covariance matrix estimates of stationary processes. A precise order of magnitude is derived for spectral radius of sample covariance matrices. We also consider a thresholded covariance matrix…
This work aims to solve a stochastic nonconvex nonsmooth composite optimization problem. Previous works on composite optimization problem requires the major part to satisfy Lipschitz smoothness or some relaxed smoothness conditions, which…
We consider the problem of robotic planning under uncertainty in this paper. This problem may be posed as a stochastic optimal control problem, a solution to which is fundamentally intractable owing to the infamous "curse of…
A significant challenge in motion planning is to avoid being in or near \emph{singular configurations} (\textit{singularities}), that is, joint configurations that result in the loss of the ability to move in certain directions in task…