Related papers: Computer aided solution of the invariance equation…

A solution of two-stage stochastic generalized equations is a pair: a first stage solution which is independent of realization of the random data and a second stage solution which is a function of random variables.This paper studies…

An efficient method has been developed for solving the inverse problem of Doppler-Zeeman mapping of magnetic, chemically peculiar stars. A regularized iteration method is used to simultaneously solve the integral equations for the Stokes I,…

Our main objective in this paper is to develop a second-order stochastic numerical method which generalizes the well-known deterministic TR-BDF2 scheme. Since most stochastic techniques used for approximating the solution of a stochastic…

Estimating large covariance matrices has been a longstanding important problem in many applications and has attracted increased attention over several decades. This paper deals with two methods based on pre-existing works to impose sparsity…

We present calypso, a parameter-conditioned stochastic surrogate model for circumbinary accretion flows. We represent the total and individual accretion time series in a PCA basis and model the resulting coefficients as draws from a…

This paper considers variational inequalities (VI) defined by the conditional value-at-risk (CVaR) of uncertain functions and provides three stochastic approximation schemes to solve them. All methods use an empirical estimate of the CVaR…

We extend a classical test of subsphericity, based on the first two moments of the eigenvalues of the sample covariance matrix, to the high-dimensional regime where the signal eigenvalues of the covariance matrix diverge to infinity and…

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…

Let $p,q$ be functions on $\mathbb{R}^{N}$ satisfying $1\ll q\ll p\ll N$, we consider $p(x)$-Laplacian problems of the form \[ \left\{ \begin{array} [c]{l}% -\Delta_{p(x)}u+V(x)\vert u\vert ^{p(x)-2}u=\lambda\vert u\vert…

We introduce the notion of p*-values (p*-variables), which generalizes p-values (p-variables) in several senses. The new notion has four natural interpretations: operational, probabilistic, Bayesian, and frequentist. A main example of a…

Covariance matrices are essential cosmological probes of fundamental physics, providing information on numerous fundamental physical parameters and varying with any change in the underlying cosmology. However, this cosmology dependence,…

This work investigates the Sobolev regularity of solutions to perturbed fractional 1-Laplace equations. Under the assumption that weak solutions are locally bounded, we establish that the regularity properties are analogous to those…

In this paper we consider in a bounded domain $\Omega \subset \mathbb{R}^N$ with smooth boundary an eigenvalue problem for the negative $(p,q)$-Laplacian with a Steklov type boundary condition, where $p\in (1,\infty)$, $q\in (2,\infty)$ and…

We develop a stochastic approximation-type algorithm to solve finite state/action, infinite-horizon, risk-aware Markov decision processes. Our algorithm has two loops. The inner loop computes the risk by solving a stochastic saddle-point…

We discuss two approaches to solving the parametric (or stochastic) eigenvalue problem. One of them uses a Taylor expansion and the other a Chebyshev expansion. The parametric eigenvalue problem assumes that the matrix $A$ depends on a…

This paper presents a methodology for using varying sample sizes in sequential quadratic programming (SQP) methods for solving equality constrained stochastic optimization problems. The first part of the paper deals with the delicate issue…

Many applications require stochastic processes specified on two- or higher-dimensional domains; spatial or spatial-temporal modelling, for example. In these applications it is attractive, for conceptual simplicity and computational…

Identifying parameters in a system of nonlinear, ordinary differential equations is vital for designing a robust controller. However, if the system is stochastic in its nature or if only noisy measurements are available, standard…

A basic problem of approximation theory, the approximation of functions from the Sobolev space W_p^r([0,1]^d) in the norm of L_q([0,1]^d), is considered from the point of view of quantum computation. We determine the quantum query…

In this paper, we define the upper (resp. lower) covariance under multiple probabilities via a corresponding max-min-max (resp. min-max-min) optimization problem and the related properties of covariances are obtained. In particular, we…