Related papers: Convergence of values in optimal stopping

The celebrated Trotter approximation theorem provides a sufficient condition for the convergence of a sequence of operator semigroups in terms of the corresponding sequence of infinitesimal generators. There exist a few results on the rate…

Inspired by a recent paper of I. Grama, E. Le Page and M. Peign\'e, we consider a sequence $(g_n)_{n \geq 1}$ of i.i.d. random $d\times d$-matrices with non-negative entries and study the fluctuations of the process $(\log \vert g_n\cdots…

This work addresses the synthesis of optimal feedback control laws via machine learning. In particular, the Averaged Feedback Learning Scheme (AFLS) and a data driven method are considered. Hypotheses for each method ensuring the…

Let $M_n^{(k)}$ denote the $k$th largest maximum of a sample $(X_1,X_2,...,X_n)$ from parent $X$ with continuous distribution. Assume there exist normalizing constants $a_n>0$, $b_n\in \mathbb{R}$ and a nondegenerate distribution $G$ such…

We derive the necessary and sufficient condition for almost sure convergence of the sequence of measurable functions, and consider some applications in the theory of Fourier series and in the theory of random fields.

This paper presents a scalable method for improving the solutions of AC Optimal Power Flow (AC OPF) with respect to deviations in predicted power injections from wind and other uncertain generation resources. The focus of the paper is on…

We design efficient approximation algorithms for maximizing the expectation of the supremum of families of Gaussian random variables. In particular, let $\mathrm{OPT}:=\max_{\sigma_1,\cdots,\sigma_n}\mathbb{E}\left[\sum_{j=1}^{m}\max_{i\in…

In this paper, we prove optimal convergence rates results for regularisation methods for solving linear ill-posed operator equations in Hilbert spaces. The result generalises existing convergence rates results on optimality to general…

We document a connection between constraint reasoning and probabilistic reasoning. We present an algorithm, called {em probabilistic arc consistency}, which is both a generalization of a well known algorithm for arc consistency used in…

We study the almost-sure termination problem for probabilistic programs. First, we show that supermartingales with lower bounds on conditional absolute difference provide a sound approach for the almost-sure termination problem. Moreover,…

We investigate the stability of the equilibrium-induced optimal value in one-dimensional diffusion setting for a time-inconsistent stopping problem under non-exponential discounting. We show that the optimal value is semi-continuous with…

This paper investigates the optimal ergodic sublinear convergence rate of the relaxed proximal point algorithm for solving monotone variational inequality problems. The exact worst case convergence rate is computed using the performance…

Gaussian random processes which variances reach theirs maximum values at unique points are considered. Exact asymptotic behaviors of probabilities of large absolute maximums of theirs trajectories have been evaluated using Double Sum Method…

A general theory is provided delivering convergence of maximal cyclically monotone mappings containing the supports of coupling measures of sequences of pairs of possibly random probability measures on Euclidean space. The theory is based…

Let (X_n,Y_n) be i.i.d. random vectors. Let W(x) be the partial sum of Y_n just before that of X_n exceeds x>0. Motivated by stochastic models for neural activity, uniform convergence of the form $\sup_{c\in I}|a(c,x)\operatorname…

We consider the optimal prediction problem of stopping a spectrally negative L\'evy process as close as possible to a given distance $b \geq 0$ from its ultimate supremum, under a squared error penalty function. Under some mild conditions,…

We provide the first quantitative estimates for the rate of convergence in the free multiplicative central limit theorem (CLT), in terms of the Kolmogorov and $r$-Wasserstein distances for $r \geq 1$. While the free additive CLT has been…

Researchers from different areas have independently defined extensions of the usual weak convergence of laws of stochastic processes with the goal of adequately accounting for the flow of information. Natural approaches are convergence of…

In this paper, convergence for moments of powered normal extremes is considered under an optimal choice of normalizing constants. It is shown that the rates of convergence for normalized powered normal extremes depend on the power index.…

Higher levels of renewable electricity generation increase uncertainty in power system operation. To ensure secure system operation, new tools that account for this uncertainty are required. In this paper, we formulate a chance-constrained…