How heterogeneous multiscale methods (HMM) handle fluctuations acting on the slow variables in fast–slow systems is investigated. In particular, it is shown via analysis of central limit theorem (CLT) and large deviation principle (LDP) that the standard version of HMM artificially amplifies these fluctuations. A simple modification of HMM, termed parallel HMM, is introduced and is shown to rem...

MARTINGALE CENTRAL LIMIT THEOREM FOR NONUNIFORMLY HYPERBOLIC SYSTEMS SEPTEMBER 2013 LUKE MOHR, B.S., UNIVERSITY AT BUFFALO M.S., UNIVERSITY OF MASSACHUSETTS AMHERST Ph.D., UNIVERSITY OF MASSACHUSETTS AMHERST Directed by: Professor HONG-KUN ZHANG In this thesis we study the central limit theorem (CLT) for nonuniformly hyperbolic dynamical systems. We examine cases in which polynomial decay of co...

Title of Document: EVALUATION OF LEACHING PROTOCOLS FOR THE TESTING OF COAL COMBUSTION BYPRODUCTS Jason Louis Becker, Master of Science, 2010 Directed By: Associate Professor Ahmet Aydilek, Department of Civil and Environmental Engineering Beneficial reuse of coal combustion byproducts requires an evaluation of metal leaching potential. Reuse of high carbon fly ash in highway embankment constru...

Let T be a rooted Galton-Watson tree with offspring distribution {pk} that has p0 = 0, mean m = P kpk > 1 and exponential tails. Consider the λ-biased random walk {Xn}n≥0 on T ; this is the nearest neighbor random walk which, when at a vertex v with dv offspring, moves closer to the root with probability λ/(λ + dv), and moves to each of the offspring with probability 1/(λ+dv). It is known that ...

Consider throwing n balls at random into m urns, each ball landing in urn i with probability pi . Let S be the resulting number of singletons, i.e., urns containing just one ball. We give an error bound for the Kolmogorov distance from the distribution of S to the normal, and estimates on its variance. These show that if n, m and (pi , 1 ≤ i ≤ m) vary in such a way that supi pi = O(n−1), then S...

This paper investigates the effects of unequal compressive and tensile moduli of carbon fibre reinforced plastic (CFRP) composites. The basic assumption is based on the statistics that the compressive modulus is a fraction lower than the tensile modulus. Data evaluated by Finite Element Analysis (FEA) model, Classical Laminate Theory (CLT) model, and experiment are used to investigate these eff...

We establish existence of Stein kernels for probability measures on R satisfying a Poincaré inequality, and obtain bounds on the Stein discrepancy of such measures. Applications to quantitative central limit theorems are discussed, including a new CLT in Wasserstein distance W2 with optimal rate and dependence on the dimension. As a byproduct, we obtain a stable version of an estimate of the Po...

Although the approximations based on the central limit theorem (CLT) for the detection probability (Pd) of the energy detector and of its more generalized cousin, the p-norm detector, are accurate for large sample sizes, their accuracy is poor otherwise. A recent work has addressed this problem by developing a cube-of-Gaussian approximation (CGA). However, CGA may not be the only option and thu...