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Saddlepoint Approximation for Moments of Random Variables
Saddlepoint Approximation Higher moments Sums of i.i.d.ran- dom variables
2016/1/19
In this paper we introduce a saddlepoint approximation method for higher-order moments like E(S − a) m+ ,a > 0, where the random variable S in these expectations could be a single random variabl...
Approximation of bivariate copulas by patched bivariate Fréchet copulas
Bivariate Fréchet copulas patched bivariate Fréchet copula approximation of bivariate copulas
2016/1/19
Bivariate Fréchet (BF) copulas characterize dependence as a mixture of three simple structures: comonotonicity, in-dependence and countermonotonicity. They are easily interpretable but have limitation...
A Rank Minimization Heuristic with Application to Minimum Order System Approximation
Rank Minimization Heuristic Minimum Order System Approximation
2015/7/10
Several problems arising in control system analysis and design, such as reduced order controller synthesis, involve minimizing the rank of a matrix variable subject to linear matrix inequality (LMI) c...
An Ellipsoidal Approximation to the Hadamard Product of Ellipsoids
Ellipsoidal Approximation Hadamard Product Ellipsoids
2015/7/10
This paper introduces a computationally efficient outer approximation to the Hadamard, i.e., element-wise, product of two ellipsoids. This element-wise product corresponds to multiplicative uncertaint...
A Diffusion Approximation for a Network of Reservoirs with Power Law Release Rule
Diffusion network reservoir power law
2015/7/8
A diffusion approximation for a network of continuous time reservoirs with power law release rules is examined. Under a mild assumption on the inflow processes, we show that for physically reasonable ...
Confidence Regions for Stochastic Approximation Algorithms
Confidence Regions Stochastic Approximation Algorithms
2015/7/8
In principle, known central limit theorems for stochastic approximation schemes permit the simulationist to provide confidence regions for both the optimum and optimizer of a stochastic optimization p...
A Diffusion Approximation for a Markovian Queue with Reneging
Markovian queues reneging impatience deadlines refl ected Ornstein–Uhlenbeck process
2015/7/8
Consider a single-server queue with a Poisson arrival process and exponential processing times in which each customer independently reneges after an exponentially distributed amount of time. We establ...
A Diffusion Approximation with a GI/GI/1 Queue with Balking or Reneging
deadlines reneging balking impatience GI/GI/1-GI queue Ornstein-Uhlenbeck process
2015/7/6
Consider a single-server queue with a renewal arrival process and generally distributed processing times in which each customer independently reneges if service has not begun within a generally distri...
Analysis of a Stochastic Approximation Algorithm for Computing Quasi-stationary Distributions
Stochastic approximations quasi-stationary distribution ODE method.
2015/7/6
This paper analyzes the convergence properties of an iterative Monte Carlo procedure proposed in the Physics literature for estimating the quasi-stationary distribution on a transient set of a Markov ...
Approximation of Solitons in the Discrete NLS Equation
Discrete soliton one dimensional discrete nonlinear schrodinger equation
2014/12/24
We study four different approximations for finding the profile of discrete solitons in the one- dimensional Discrete Nonlinear Schrödinger (DNLS) Equation. Three of them are discrete approximatio...
Approximation of epidemic models by diffusion processes and their statistical inference
Approximation epidemic models diffusion processes their statistical inference
2013/6/14
Among various mathematical frameworks, multidimensional continuous-time Markov jump processes $(Z_t)$ on $\N^d$ form a natural set-up for modeling $SIR$-like epidemics. In this study we extend the res...
On Approximation of the Backward Stochastic Differential Equation
Backward SDE approximation of the solution small noise asymptotics
2013/6/14
We consider the problem of approximation of the solution of the backward stochastic differential equation in the Markovian case. We suppose that the trend coefficient of the diffusion process depends ...
Efficient Density Estimation via Piecewise Polynomial Approximation
Efficient Density Estimation Piecewise Polynomial Approximation
2013/6/14
We give a highly efficient "semi-agnostic" algorithm for learning univariate probability distributions that are well approximated by piecewise polynomial density functions. Let $p$ be an arbitrary dis...
A least-squares method for sparse low rank approximation of multivariate functions
least-squares method sparse low rank approximation multivariate functions
2013/6/14
In this paper, we propose a low-rank approximation method based on discrete least-squares for the approximation of a multivariate function from random, noisy-free observations. Sparsity inducing regul...
Universal Approximation Depth and Errors of Narrow Belief Networks with Discrete Units
Deep belief network restricted Boltzmann machine universal approxima-tion representational power Kullback-Leibler divergence,q-ary variable
2013/4/28
We generalize recent theoretical work on the minimal number of layers of narrow deep belief networks that can approximate any probability distribution on the states of their visible units arbitrarily ...