Related papers: Central Limit Theorems for Sample Average Approxim…
Stochastic Approximation (SA) is a popular approach for solving fixed-point equations where the information is corrupted by noise. In this paper, we consider an SA involving a contraction mapping with respect to an arbitrary norm, and show…
Two-time-scale Stochastic Approximation (SA) is an iterative algorithm with applications in reinforcement learning and optimization. Prior finite time analysis of such algorithms has focused on fixed point iterations with mappings…
We consider optimal allocation problems with Conditional Value-At-Risk (CVaR) constraint. We prove, under very mild assumptions, the convergence of the Sample Average Approximation method (SAA) applied to this problem, and we also exhibit a…
We determine the asymptotic distribution of the sum of correlated variables described by a matrix product ansatz with finite matrices, considering variables with finite variances. In cases when the correlation length is finite, the law of…
Approximating the solution of the nonlinear filtering problem with Gaussian mixtures has been a very popular method since the 1970s. However, the vast majority of such approximations are introduced in an ad-hoc manner without theoretical…
We establish statistical limit theorems for equilibrium states of Axiom A diffeomorphisms, derived from the spectral gap of the Ruelle transfer operator established in Part I (Thiam2026a) and transferred to smooth dynamics through the…
We consider a nonlinear discrete stochastic control system, and our goal is to design a feedback control policy in order to lead the system to a prespecified state. We adopt a stochastic approximation viewpoint of this problem. It is known…
Stochastic approximation (SA) is a powerful class of iterative algorithms for nonlinear root-finding that can be used for minimizing a loss function, $L(\boldsymbol{\theta})$, with respect to a parameter vector $\boldsymbol{\theta}$, when…
We study the central limit theorem in the non-normal domain of attraction to symmetric $\alpha$-stable laws for $0<\alpha\leq2$. We show that for i.i.d. random variables $X_i$, the convergence rate in $L^\infty$ of both the densities and…
We study optimization for data-driven decision-making when we have observations of the uncertain parameters within the optimization model together with concurrent observations of covariates. Given a new covariate observation, the goal is to…
We analyze the optimal policy for the sequential selection of an alternating subsequence from a sequence of $n$ independent observations from a continuous distribution $F$, and we prove a central limit theorem for the number of selections…
We study a statistical method to estimate the optimal value, and the optimality gap of a given solution for stochastic optimization as an assessment of the solution quality. Our approach is based on bootstrap aggregating, or bagging,…
Data-driven control of discrete-time and continuous-time systems is of tremendous research interest. In this paper, we explore data-driven optimal control of continuous-time linear systems using input-output data. Based on a density result,…
A non-classical formulation of the central limit theorem is given for sequences of independent random variables with finite second moments. Singular sequences whose members all have a degenerate or normal distribution are excluded from…
This paper presents the asymptotic theory for nondegenerate $U$-statistics of high frequency observations of continuous It\^{o} semimartingales. We prove uniform convergence in probability and show a functional stable central limit theorem…
Recently, we and several other authors have written about the possibilities of using stochastic approximation techniques for fitting variational approximations to intractable Bayesian posterior distributions. Naive implementations of…
In this work, we study the stochastic optimal control problem (SOC) mainly from the probabilistic view point, i.e. via the Stochastic Maximum principle (SMP) \cite{Peng4}. We adopt the sample-wise backpropagation scheme proposed in…
In this note we consider the finite-dimensional parameter estimation problem associated to inverse problems. In such scenarios, one seeks to maximize the marginal likelihood associated to a Bayesian model. This latter model is connected to…
We study the number of occurrences of any fixed vincular permutation pattern. We show that this statistics on uniform random permutations is asymptotically normal and describe the speed of convergence. To prove this central limit theorem,…
Recent theoretical works have characterized the dynamics of wide shallow neural networks trained via gradient descent in an asymptotic mean-field limit when the width tends towards infinity. At initialization, the random sampling of the…