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We consider stochastic zero-order optimization problems, which arise in settings from simulation optimization to reinforcement learning. We propose an adaptive sampling quasi-Newton method where we estimate the gradients of a stochastic…

Optimization and Control · Mathematics 2019-10-31 Raghu Bollapragada , Stefan M. Wild

We consider a single-server queue where interarrival and service times depend linearly and randomly on customer waiting times, and establish a sample-path moderate deviation principle (MDP) for the waiting time process. The waiting times…

Probability · Mathematics 2025-11-03 Chang Feng , John J. Hasenbein , Guodong Pang

This note provides a tool to infer moderate deviations principles for specific random variables from deviations principles for their Hubbard-Stratonovich transforms.

Probability · Mathematics 2012-10-03 Matthias Löwe , Raphael Meiners

Self-normalized processes arise naturally in statistical applications. Being unit free, they are not affected by scale changes. Moreover, self-normalization often eliminates or weakens moment assumptions. In this paper we present several…

Probability · Mathematics 2007-05-23 Victor H. de la Pena , Michael J. Klass , Tze Leung Lai

We consider Riemann sum approximations of stochastic integrals with respect to the fractional Browian motion of index $H\geq \frac12$. We show the convergence of these schemes at first and second order. The processes obtained in the limit…

Probability · Mathematics 2021-12-20 Valentin Garino , Ivan Nourdin , Pierre Vallois

In this paper, we aim to study the asymptotic behavior for multi-scale McKean-Vlasov stochastic dynamical systems. Firstly, we obtain a central limit type theorem, i.e, the deviation between the slow component $X^{\varepsilon}$ and the…

Probability · Mathematics 2023-06-02 Wei Hong , Shihu Li , Wei Liu , Xiaobin Sun

Stochastic Approximation has been a prominent set of tools for solving problems with noise and uncertainty. Increasingly, it becomes important to solve optimization problems wherein there is noise in both a set of constraints that a…

Optimization and Control · Mathematics 2025-07-29 Francisco Facchinei , Vyacheslav Kungurtsev

In this paper, moderate deviations for normal approximation of functionals over infinitely many Rademacher random variables are derived. They are based on a bound for the Kolmogorov distance between a general Rademacher functional and a…

Probability · Mathematics 2024-06-12 Marius Butzek , Peter Eichelsbacher , Benedikt Rednoß

We apply Lindeberg's method, invented to prove a central limit theorem, to analyze the moderate deviations around such a central limit theorem. In particular, we will show moderate deviation principles for martingales as well as for random…

Probability · Mathematics 2018-10-03 Peter Eichelsbacher , Matthias Löwe

The semimartingale stochastic approximation procedure, namely, the Robbins-Monro type SDE is introduced which naturally includes both generalized stochastic approximation algorithms with martingale noises and recursive parameter estimation…

Probability · Mathematics 2007-05-23 N. Lazrieva , T. Sharia , T. Toronjadze

We propose an unconstrained stochastic approximation method of finding the optimal measure change (in an a priori parametric family) for Monte Carlo simulations. We consider different parametric families based on the Girsanov theorem and…

Probability · Mathematics 2018-02-20 Vincent Lemaire , Gilles Pagès

This paper proposes and analyzes fully data driven methods for inference about the mean function of a stochastic process from a sample of independent trajectories of the process, observed at discrete time points and corrupted by additive…

Methodology · Statistics 2009-05-20 F. Bunea , M. H. Wegkamp , A. E. Ivanescu

In this article, we develop a framework to study the large deviation principle for matrix models and their quantized versions, by tilting the measures using the limits of spherical integrals obtained in [46,47]. As examples, we obtain 1. a…

Probability · Mathematics 2023-04-25 Serban Belinschi , Alice Guionnet , Jiaoyang Huang

We consider stochastic approximations which arise from such applications as data communications and image processing. We demonstrate why constraints are needed in a stochastic approximation and how a constrained approximation can be…

Numerical Analysis · Mathematics 2015-09-01 Hong Jiang , Gang Huang , Paul Wilford , Liangkai Yu

In this article we establish Cram\'er type moderate deviation results for (intermediate) trimmed means $T_n=n^{-1} \sum_{i=k_n+1}^{n-m_n}X_{i:n}$, where $X_{i:n}$ -- the order statistics corresponding to the first $n$ observations of…

Probability · Mathematics 2016-08-09 Nadezhda Gribkova

We establish a central limit theorem and prove a moderate deviation principle for stochastic scalar conservation laws. Due to the lack of viscous term, this is done in the framework of kinetic solution. The weak convergence method and…

Probability · Mathematics 2022-08-31 Zhengyan Wu , Rangrang Zhang

The Adaptive Multilevel Splitting (AMS) algorithm is a powerful and versatile method for the simulation of rare events. It is based on an interacting (via a mutation-selection procedure) system of replicas, and depends on two integer…

Probability · Mathematics 2015-02-25 Charles-Edouard Bréhier

The Pseudo-Marginal (PM) algorithm is a popular Markov chain Monte Carlo (MCMC) method used to sample from a target distribution when its density is inaccessible, but can be estimated with a non-negative unbiased estimator. Its performance…

Computation · Statistics 2025-09-30 Sarra Abaoubida , Mylène Bédard , Florian Maire

We study pathwise approximation of scalar stochastic differential equations at a single point. We provide the exact rate of convergence of the minimal errors that can be achieved by arbitrary numerical methods that are based (in a…

Probability · Mathematics 2007-05-23 Thomas Muller-Gronbach

This work brings together two powerful concepts in Gaussian processes: the variational approach to sparse approximation and the spectral representation of Gaussian processes. This gives rise to an approximation that inherits the benefits of…

Machine Learning · Statistics 2017-11-09 James Hensman , Nicolas Durrande , Arno Solin