Related papers: Rayleigh-Ritz variational method with suitable asy…
We study a family of polynomials which are orthogonal with respect to the varying, highly oscillatory complex weight function $e^{ni\lambda z}$ on $[-1,1]$, where $\lambda$ is a positive parameter. This family of polynomials has appeared in…
We obtain results on both weak and almost sure asymptotic behaviour of power variations of a linear combination of independent Wiener process and fractional Brownian motion. These results are used to construct strongly consistent parameter…
This paper deals with the estimation of reliability $R=P(Y<X)$ when $X$ is a random strength of a component subjected to a random stress $Y$ and $(X,Y)$ follows a bivariate Rayleigh distribution. The maximum likelihood estimator of $R$ and…
We study a one-parameter family of probability measures on lozenge tilings of large regular hexagons that interpolates between the uniform measure on all possible tilings and a particular fully frozen tiling. The description of the…
We present applications of variational -- wavelet approach to different forms of nonlinear (rational) rms envelope equations. We have the representation for beam bunch oscillations as a multiresolution (multiscales) expansion in the base of…
This short report gives a non-asymptotic rate of convergence proof for solving a two-block coordinate descent problem. This non-asymptotic proof is a simple result that can be derived easily from available results in the literature. We give…
We introduce a variational method for approximating distribution functions of dynamics with a ``Liouville operator'' $\hL,$ in terms of a {\em nonequilibrium action functional} for two independent (left and right) trial states. The method…
Randomized Controlled Trials (RCT) are the current gold standards to empirically measure the effect of a new drug. However, they may be of limited size and resorting to complementary non-randomized data, referred to as observational, is…
We develop new solvability methods for divergence form second order, real and complex, elliptic systems above Lipschitz graphs, with $L_2$ boundary data. The coefficients $A$ may depend on all variables, but are assumed to be close to…
Let X_R be the zero locus in RP^n of one or two independently and Weyl distributed random real quadratic forms (this is the same as requiring that the corresponding symmetric matrices are in the Gaussian Orthogonal Ensemble). We prove that…
This paper develops an asymptotic distribution theory for an endogenous instrumentation approach in quantile predictive regressions when both generated covariates and persistent predictors are used. The generated covariates are obtained…
The inertial collapse of two interacting and non-translating spherical bubbles of equal size is considered. The exact analytic solution to the nonlinear ordinary differential equation that governs the bubble radii during collapse is first…
We derive the precise asymptotic distributional behavior of Gaussian variational approximate estimators of the parameters in a single-predictor Poisson mixed model. These results are the deepest yet obtained concerning the statistical…
We study the quadratic prediction error method -- i.e., nonlinear least squares -- for a class of time-varying parametric predictor models satisfying a certain identifiability condition. While this method is known to asymptotically achieve…
This paper studies formulations of second-order elliptic partial differential equations in nondivergence form on convex domains as equivalent variational problems. The first formulation is that of Smears \& S\"uli [SIAM J.\ Numer.\ Anal.\…
In this paper we study the asymptotics of linear regression in settings with non-Gaussian covariates where the covariates exhibit a linear dependency structure, departing from the standard assumption of independence. We model the covariates…
We introduce some new indexes to measure the departure of any multivariate continuous distribution on non-negative orthant from a given reference one such the uncorrelated exponential model, similar to the relative Fisher dispersion indexes…
We obtain the strong asymptotics of polynomials $p_n(\lambda)$, $\lambda\in\mathbb{C}$, orthogonal with respect to measures in the complex plane of the form $$ e^{-N(|\lambda|^{2s}-t\lambda^s-\overline{t\lambda}^s)}dA(\lambda), $$ where $s$…
In this paper we compute the asymptotic behavior of the recurrence coefficients for polynomials orthogonal with respect to a logarithmic weight $w(x){\rm d}x = \log \frac{2k}{1-x}{\rm d}x$ on $(-1,1)$, $k > 1$, and verify a conjecture of…
Variational inequalities offer a versatile and straightforward approach to analyzing a broad range of equilibrium problems in both theoretical and practical fields. In this paper, we consider a composite generally non-monotone variational…