Related papers: On truncated variation, upward truncated variation…
We approximate stochastic processes in finite dimension by dynamical systems. We provide trajectorial estimates which are uniform with respect to the initial condition for a well chosen distance. This relies on some non-expansivity property…
Seifert derived an exact fluctuation relation for diffusion processes using the concept of "stochastic system entropy". In this note we extend his formalism to entropic transport. We introduce the notion of relative stochastic entropy, or…
The total variation distance is a metric of central importance in statistics and probability theory. However, somewhat surprisingly, questions about computing it algorithmically appear not to have been systematically studied until very…
In this paper we develop new applications of variational analysis and generalized differentiation to the following optimization problem and its specifications: given n closed subsets of a Banach space, find such a point for which the sum of…
We consider three mathematically equivalent variants of the conjugate gradient (CG) algorithm and how they perform in finite precision arithmetic. It was shown in [{\em Behavior of slightly perturbed Lanczos and conjugate-gradient…
The accurate estimation of scaling exponents is central in the observational study of scale-invariant phenomena. Natural systems unavoidably provide observations over restricted intervals; consequently a stationary stochastic process (time…
Mirror Descent is a popular algorithm, that extends Gradients Descent (GD) beyond the Euclidean geometry. One of its benefits is to enable strong convergence guarantees through smooth-like analyses, even for objectives with exploding or…
Empirical risk minimization over classes functions that are bounded for some version of the variation norm has a long history, starting with Total Variation Denoising (Rudin et al., 1992), and has been considered by several recent articles,…
We show that a substantial portion of stochastic calculus can be developed along similar lines to ordinary calculus, with derivative-based concepts driving the development. We define a notion of stopping derivative, which is a form of right…
This article addresses structure-preserving smooth approximation of semiconcave functions. semiconcave functions are of particular interest because they naturally arise in a variety of variational problems, including {optimal feedback…
We introduce a stochastic fractional calculus. As an application, we present a stochastic fractional calculus of variations, which generalizes the fractional calculus of variations to stochastic processes. A stochastic fractional…
The theory of stochastic approximations form the theoretical foundation for studying convergence properties of many popular recursive learning algorithms in statistics, machine learning and statistical physics. Large deviations for…
Let $T\subset\mathbb{R}$ and $(X,\mathcal{U})$ be a uniform space with an at most countable gage of pseudometrics $\{d_p:p\in\mathcal{P}\}$ of the uniformity $\mathcal{U}$. Given $f\in X^T$ (=the family of all functions from $T$ into $X$),…
Total variation distance (TV distance) is an important measure for the difference between two distributions. Recently, there has been progress in approximating the TV distance between product distributions: a deterministic algorithm for a…
Controlled one-dimensional diffusion processes, with infinitesimal variance (instead of the infinitesimal mean) depending on the control variable, are considered in an interval located on the positive half-line. The process is controlled…
The cutoff phenomenon describes the case when an abrupt transition occurs in the convergence of a Markov chain to its equilibrium measure. There are various metrics which can be used to measure the distance to equilibrium, each of which…
This paper considers a continuous time analogue of the classical autoregressive moving average processes, L\'evy-driven CARMA processes. First we describe limiting properties of the periodogram by means of the so-called truncated Fourier…
Using a microfluidics device filled with a colloidal suspension of microspheres, we test the laws of diffusion in the limit of small particle numbers. Our focus is not just on average properties such as the mean flux, but rather on the…
We propose an extragradient method with stepsizes bounded away from zero for stochastic variational inequalities requiring only pseudo-monotonicity. We provide convergence and complexity analysis, allowing for an unbounded feasible set,…
We consider the mean-variance hedging problem under partial Information. The underlying asset price process follows a continuous semimartingale and strategies have to be constructed when only part of the information in the market is…