Related papers: Large deviation inequalities for the nonlinear unb…

This paper presents two stochastic model predictive control methods for linear time-invariant systems subject to unbounded additive uncertainties. The new methods are developed by formulating the chance constraints into deterministic form,…

We consider the problem of estimating the state and unknown input for a large class of nonlinear systems subject to unknown exogenous inputs. The exogenous inputs themselves are modeled as being generated by a nonlinear system subject to…

In this paper, state and noise covariance estimation problems for linear system with unknown multiplicative noise are considered. The measurement likelihood is modelled as a mixture of two Gaussian distributions and a Student's t…

We collect, survey and develop methods of (one-dimensional) stochastic approximation in a framework that seems suitable to handle fairly broad generalizations of Polya urns. To show the applicability of the results we determine the limiting…

We obtain large and moderate deviation estimates, as well as concentration inequalities, for a class of nonuniformly expanding maps with stretched exponential decay of correlations. In the large deviation regime, we also exhibit examples…

The Kalman filter is an established tool for the analysis of dynamic systems with normally distributed noise, and it has been successfully applied in numerous application areas. It provides sequentially calculated estimates of the system…

In this paper, the problem of state estimation, in the context of both filtering and smoothing, for nonlinear state-space models is considered. Due to the nonlinear nature of the models, the state estimation problem is generally intractable…

This article introduces a new class of fast algorithms to approximate variational problems involving unbalanced optimal transport. While classical optimal transport considers only normalized probability distributions, it is important for…

This paper introduces the Non-linear Partition of Unity Method, a novel technique integrating Radial Basis Function interpolation and Weighted Essentially Non-Oscillatory algorithms. It addresses challenges in high-accuracy approximations,…

Bayesian calibration of computer models tunes unknown input parameters by comparing outputs with observations. For model outputs that are distributed over space, this becomes computationally expensive because of the output size. To overcome…

We consider an inverse problem arising in nonlinear ultrasound imaging. The propagation of ultrasound waves is modeled by a quasilinear wave equation. We make measurements at the boundary of the medium encoded in the Dirichlet-to-Neumann…

We develop a multi-level restricted Gaussian maximum likelihood method for estimating the covariance function parameters and computing the best unbiased predictor. Our approach produces a new set of multi-level contrasts where the…

A basic experiment in probability theory is drawing without replacement from an urn filled with multiple balls of different colours. Clearly, it is physically impossible to overdraw, that is, to draw more balls from the urn than it…

The random self-reinforcement mechanism, characterized by the principle of ``the rich get richer'', has demonstrated significant utility across various domains. One prominent model embodying this mechanism is the random reinforcement urn…

Deep learning has the potential to dramatically impact navigation and tracking state estimation problems critical to autonomous vehicles and robotics. Measurement uncertainties in state estimation systems based on Kalman and other Bayes…

A Lagrange multiplier theorem is derived for the case of an imprecise objective function and a precise constraint. The proof uses methods of analysis which deal in a direct, algebraic way with imprecisions. They include imprecise…

In this work we consider the \emph{infinite color urn model} associated with a bounded increment random walk on $\Zbold^d$. This model was first introduced by Bandyopadhyay and Thacker (2013). We prove that the rate of convergence of the…

We consider a multivalued nonlinear Duffing system driven by a nonlinear nonhomogeneous differential operator. We prove existence theorems for both the convex and nonconvex problems (according to whether the multivalued perturbation is…

We study the approximation of functions which are invariant with respect to certain permutations of the input indices using flow maps of dynamical systems. Such invariant functions includes the much studied translation-invariant ones…

We investigate an additive perturbation of a complex Wishart random matrix and prove that a large deviation principle holds for the spectral measures. The rate function is associated to a vector equilibrium problem coming from logarithmic…