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The normal or Gaussian distribution plays a prominent role in almost all fields of science. However, it is well known that the Gauss (or Euler--Poisson) integral over a finite boundary, as it is necessary for instance for the error function…
We consider the problem of numerically evaluating the expected value of a smooth bounded function of a chi-distributed random variable, divided by the square root of the number of degrees of freedom. This problem arises in the contexts of…
This paper studies the application of the blended dynamics approach towards distributed optimization problem where the global cost function is given by a sum of local cost functions. The benefits include (i) individual cost function need…
In this paper we propose a novel Bayesian methodology for Value-at-Risk computation based on parametric Product Partition Models. Value-at-Risk is a standard tool to measure and control the market risk of an asset or a portfolio, and it is…
Over the last few years there have been dramatic advances in our understanding of mathematical and computational models of complex systems in the presence of uncertainty. This has led to a growth in the area of uncertainty quantification as…
Many combinatorial generating functions can be expressed as combinations of symmetric functions, or extracted as sub-series and specializations from such combinations. Gessel has outlined a large class of symmetric functions for which the…
It is known, but perhaps not well-known, that when the mortality is assumed to be of Gompertz-Makeham-type, the expected remaining life-length and the commutation functions used for calculating the expected values of various types of life…
We investigate the theoretical foundations of the simulated tempering method and use our findings to design efficient algorithms. Employing a large deviation argument first used for replica exchange molecular dynamics [Plattner et al., J.…
We study a Grushin critical problem in a strip domain which satisfies the periodic boundary conditions. By applying the finite-dimensional reduction method, we construct a periodic solution when the prescribed curvature function is…
We show that an interesting class of functionals of stochastic differential equations can be approximated by a Chen-Fliess series of iterated stochastic integrals and give a L^{2} error estimate, thus generalizing the standard stochastic…
The present paper continues our investigation of an implementation of a least-squares collocation method for higher-index differential-algebraic equations. In earlier papers, we were able to substantiate the choice of basis functions and…
This paper solves the Sylvester equation in the form of AX+XB=C in a distributed way, and proposes three distributed continuous-time algorithms for three cases. We start with the basic algorithm for solving a least squares solution of the…
In this paper we describe a theory of a cumulative distribution function on a space with an order from a probability measure defined in this space. This distribution function plays a similar role to that played in the classical case.…
We consider the cubic nonlinear fourth-order Schr\"odinger equation \[ i\partial_t u - \Delta^2 u + \mu \Delta u = \pm |u|^2 u, \quad \mu \geq 0 \] on $\mathbb{R}^N, N \geq 5$ with random initial data. We prove almost sure local…
A central problem in computational statistics is to convert a procedure for sampling combinatorial from an objects into a procedure for counting those objects, and vice versa. Weconsider sampling problems coming from *Gibbs distributions*,…
Probability distributions which can be obtained from superpositions of Gaussian distributions of different variances v = \sigma ^2 play a favored role in quantum theory and financial markets. Such superpositions need not necessarily obey…
In this paper, we introduce the cubature formula for Stochastic Volterra Integral Equations. We first derive the stochastic Taylor expansion in this setting, by utilizing a functional It\^{o} formula, and provide its tail estimates. We then…
We study the statistical complexity of estimating partition functions given sample access to a proposal distribution and an unnormalized density ratio for a target distribution. While partition function estimation is a classical problem,…
In this work, we study a new approach to optimizing the margin distribution realized by binary classifiers. The classical approach to this problem is simply maximization of the expected margin, while more recent proposals consider…
The convergence analysis of a third-order scheme for the highly nonlinear Landau-Lifshitz-Gilbert equation with a non-convex constraint is considered. In this paper, we first present a fully discrete semi-implicit method for solving the…