Analysis Commons^™

Agnostic Science. Towards A Philosophy Of Data Analysis, Domenico Napoletani, Marco Panza, Daniele C. Struppa

MPP Published Research

In this paper we will offer a few examples to illustrate the orientation of contemporary research in data analysis and we will investigate the corresponding role of mathematics. We argue that the modus operandi of data analysis is implicitly based on the belief that if we have collected enough and sufficiently diverse data, we will be able to answer most relevant questions concerning the phenomenon itself. This is a methodological paradigm strongly related, but not limited to, biology, and we label it the microarray paradigm. In this new framework, mathematics provides powerful techniques and general ideas which generate new …

An Anticipative Stochastic Calculus Approach To Pricing In Markets Driven By Lévy Process, Bernt Øksendal, Agnès Sulem

Communications on Stochastic Analysis

No abstract provided.

Preface

Communications on Stochastic Analysis

No abstract provided.

Persistence Of Invertibility In The Wiener Space, A S Üstünel

Communications on Stochastic Analysis

No abstract provided.

The Asymptotic Dependence Behavior Of Ornstein-Uhlenbeck Semi-Stable Processes, Balram S Rajput

Communications on Stochastic Analysis

No abstract provided.

Set-Valued Stochastic Differential Equation In M-Type 2 Banach Space, Itaru Mitoma, Yoshiaki Okazaki, Jinping Zhang

Communications on Stochastic Analysis

No abstract provided.

On The Non-Classical Infinite Divisibility Of Power Semicircle Distributions, Octavio Arizmendi, Victor Pérez-Abreu

Communications on Stochastic Analysis

No abstract provided.

Stochastic Magneto-Hydrodynamic System Perturbed By General Noise, P Sundar

Communications on Stochastic Analysis

No abstract provided.

What Is A Gaussian State?, K R Parthasarathy

Communications on Stochastic Analysis

No abstract provided.

A Stochastic Finite Element Method For Stochastic Parabolic Equations Driven By Purely Spatial Noise, Chia Ying Lee, Boris Rozovskii

Communications on Stochastic Analysis

No abstract provided.

Wavelet Transform Of Fractional Integrals For Integrable Boehmians, Deshna Loonker, P. K. Banerji, S. L. Kalla

Applications and Applied Mathematics: An International Journal (AAM)

The present paper deals with the wavelet transform of fractional integral operator (the Riemann- Liouville operators) on Boehmian spaces. By virtue of the existing relation between the wavelet transform and the Fourier transform, we obtained integrable Boehmians defined on the Boehmian space for the wavelet transform of fractional integrals.

Convergence Of The Sinc Method Applied To Volterra Integral Equations, M. Zarebnia, J. Rashidinia

Applications and Applied Mathematics: An International Journal (AAM)

A collocation procedure is developed for the linear and nonlinear Volterra integral equations, using the globally defined Sinc and auxiliary basis functions. We analytically show the exponential convergence of the Sinc collocation method for approximate solution of Volterra integral equations. Numerical examples are included to confirm applicability and justify rapid convergence of our method.

An Efficient Technique For Solving Special Integral Equations, Jafar Biazar, Mostafa Eslami

Applications and Applied Mathematics: An International Journal (AAM)

In this paper, we apply a new technique for solving two-dimensional integral equations of mixed type. Comparisons are made between the homotopy perturbation method and the new technique. The results reveal that the new technique is effective and convenient.

Noncommutative Topology And The World’S Simplest Index Theorem, Erik Van Erp

Dartmouth Scholarship

In this article we outline an approach to index theory on the basis of methods of noncommutative topology. We start with an explicit index theorem for second-order differential operators on 3-manifolds that are Fredholm but not elliptic. This low-brow index formula is expressed in terms of winding numbers. We then proceed to show how it is derived as a special case of an index theorem for hypoelliptic operators on contact manifolds. Finally, we discuss the noncommutative topology that is employed in the proof of this theorem. The article is intended to illustrate that noncommutative topology can be a powerful tool …

Rao's Quadratic Entropy And Some New Applications, Yueqin Zhao

Mathematics & Statistics Theses & Dissertations

Many problems in statistical inference are formulated as testing the diversity of populations. The entropy functions measure the similarity of a distribution function to the uniform distribution and hence can be used as a measure of diversity. Rao (1982a) proposed the concept of quadratic entropy. Its concavity property makes the decomposition similar to ANOVA for categorical data feasible. In this thesis, after reviewing the properties and providing a modification to quadratic entropy, various applications of quadratic entropy are explored. First, analysis of quadratic entropy with the suggested modification to analyze the contingency table data is explored. Then its application to …

Preface

Communications on Stochastic Analysis

No abstract provided.

On The Existence Of Weak Variational Solutions To Stochastic Differential Equations, L Gawarecki, V Mandrekar

Communications on Stochastic Analysis

No abstract provided.

Some Solvable Classes Of Filtering Problem With Ornstein-Uhlenbeck Noise, Zhicheng Liu, Jie Xiong

Communications on Stochastic Analysis

No abstract provided.

Commutativity Properties Of Conditional Distributions And Palm Measures, Olav Kallenberg

Communications on Stochastic Analysis

No abstract provided.

Some Asymptotic Results For Near Critical Branching Processes, Amarjit Budhiraja, Dominik Reinhold

Communications on Stochastic Analysis

No abstract provided.

Uniqueness Of Solution To The Kolmogorov Forward Equation: Applications To White Noise Theory Of Filtering, Abhay G Bhatt, Rajeeva L Karandikar

Communications on Stochastic Analysis

No abstract provided.

Quasi-Exact Approximation Of Hidden Markov Chain Filters, Eckhard Platen, Renata Rendek

Communications on Stochastic Analysis

No abstract provided.

Inverse Stochastic Transfer Principle, Matthew Linn, Anna Amirdjanova

Communications on Stochastic Analysis

No abstract provided.

Risk-Based Indifference Pricing Under A Stochastic Volatility Model, Robert J Elliott, Tak Kuen Siu

Communications on Stochastic Analysis

No abstract provided.

Some New Classes Of Complex Symmetric Operators, Stephan Ramon Garcia, Warren R. Wogen

Pomona Faculty Publications and Research

We say that an operator $T \in B(H)$ is complex symmetric if there exists a conjugate-linear, isometric involution $C:H\to H$ so that $T = CT^*C$. We prove that binormal operators, operators that are algebraic of degree two (including all idempotents), and large classes of rank-one perturbations of normal operators are complex symmetric. From an abstract viewpoint, these results explain why the compressed shift and Volterra integration operator are complex symmetric. Finally, we attempt to describe all complex symmetric partial isometries, obtaining the sharpest possible statement given only the data $(\dim \ker T, \dim \ker T^*)$.

Mathematics In Motion: Linear Systems Of Differential Equations On The Differential Analyzer, Devon A. Tivener

Theses, Dissertations and Capstones

In this work, I will provide an introduction to the dierential analyzer, a machine designed to solve dierential equations through a process called mechanical integration. I will give a brief historical account of dierential analyzers of the past, and discuss the Marshall University Dierential Analyzer Project. The goal of this work is to provide an analysis of solutions of systems of dierential equations using a dierential analyzer. In particular, we are interested in the points at which these systems are in equilibrium and the behavior of solutions that start away from equilibrium. After giving a description of linear systems of …

Analysis Of Models For Longitudinal And Clustered Binary Data, Weiming Yang

Mathematics & Statistics Theses & Dissertations

This dissertation deals with modeling and statistical analysis of longitudinal and clustered binary data. Such data consists of observations on a dichotomous response variable generated from multiple time or cluster points, that exhibit either decaying correlation or equi-correlated dependence. The current literature addresses modeling the dependence using an appropriate correlation structure, but ignores the feasible bounds on the correlation parameter imposed by the marginal means.

The first part of this dissertation deals with two multivariate probability models, the first order Markov chain model and the multivariate probit model, that adhere to the feasible bounds on the correlation. For both the …

Neutrosophic Bilinear Algebras And Their Generalizations, Florentin Smarandache, W.B. Vasantha Kandasamy

Branch Mathematics and Statistics Faculty and Staff Publications

This book introduces the concept of neutrosophic bilinear algebras and their generalizations to n-linear algebras, n>2. This book has five chapters. The reader should be well-versed with the notions of linear algebras as well as the concepts of bilinear algebras and n- linear algebras. Further the reader is expected to know about neutrosophic algebraic structures as we have not given any detailed literature about it. The first chapter is introductory in nature and gives a few essential definitions and references for the reader to make use of the literature in case the reader is not thorough with the basics. …

New Classes Of Neutrosophic Linear Algebras, Florentin Smarandache, W.B. Vasantha Kandasamy, K. Ilanthenral

Branch Mathematics and Statistics Faculty and Staff Publications

In this book we introduce mainly three new classes of linear algebras; neutrosophic group linear algebras, neutrosophic semigroup linear algebras and neutrosophic set linear algebras. The authors also define the fuzzy analogue of these three structures. This book is organized into seven chapters. Chapter one is introductory in content. The notion of neutrosophic set linear algebras and neutrosophic neutrosophic set linear algebras are introduced and their properties analysed in chapter two. Chapter three introduces the notion of neutrosophic semigroup linear algebras and neutrosophic group linear algebras. A study of their substructures are systematically carried out in this chapter. The fuzzy …

Advances And Applications Of Dsmt For Information Fusion (In Chinese), Florentin Smarandache, Jean Dezert

Branch Mathematics and Statistics Faculty and Staff Publications

No abstract provided.