Stochastic Convergence
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Stochastic Convergence
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Author : Eugene Lukacs
language : en
Publisher: Academic Press
Release Date : 2014-07-03
Stochastic Convergence written by Eugene Lukacs and has been published by Academic Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-07-03 with Mathematics categories.
Stochastic Convergence, Second Edition covers the theoretical aspects of random power series dealing with convergence problems. This edition contains eight chapters and starts with an introduction to the basic concepts of stochastic convergence. The succeeding chapters deal with infinite sequences of random variables and their convergences, as well as the consideration of certain sets of random variables as a space. These topics are followed by discussions of the infinite series of random variables, specifically the lemmas of Borel-Cantelli and the zero-one laws. Other chapters evaluate the power series whose coefficients are random variables, the stochastic integrals and derivatives, and the characteristics of the normal distribution of infinite sums of random variables. The last chapter discusses the characterization of the Wiener process and of stable processes. This book will prove useful to mathematicians and advance mathematics students.
Convergence Of Stochastic Processes
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Author : D. Pollard
language : en
Publisher: David Pollard
Release Date : 1984-10-08
Convergence Of Stochastic Processes written by D. Pollard and has been published by David Pollard this book supported file pdf, txt, epub, kindle and other format this book has been release on 1984-10-08 with Mathematics categories.
Functionals on stochastic processes; Uniform convergence of empirical measures; Convergence in distribution in euclidean spaces; Convergence in distribution in metric spaces; The uniform metric on space of cadlag functions; The skorohod metric on D [0, oo); Central limit teorems; Martingales.
Stochastic Limit Theory
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Author : James Davidson
language : en
Publisher: OUP Oxford
Release Date : 1994-10-13
Stochastic Limit Theory written by James Davidson and has been published by OUP Oxford this book supported file pdf, txt, epub, kindle and other format this book has been release on 1994-10-13 with Business & Economics categories.
This is a survey of the recent developments in the rapidly expanding field of asymptotic distribution theory, with a special emphasis on the problems of time dependence and heterogeneity. The book is designed to be useful on two levels. First as a textbook and reference work, giving definitions of the relevant mathematical concepts, statements, and proofs of the important results from the probability literature, and numerous examples; and second, as an account of recent work in the field of particular interest to econometricians, including a number of important new results. It is virtually self-contained, with all but the most basic technical prerequisites being explained in their context; mathematical topics include measure theory, integration, metric spaces, and topology, with applications to random variables, and an extended treatment of conditional probability. Other subjects treated include: stochastic processes, mixing processes, martingales, mixingales, and near-epoch dependence; the weak and strong laws of large numbers; weak convergence; and central limit theorems for nonstationary and dependent processes. The functional central limit theorem and its ramifications are covered in detail, including an account of the theoretical underpinnings (the weak convergence of measures on metric spaces), Brownian motion, the multivariate invariance principle, and convergence to stochastic integrals. This material is of special relevance to the theory of cointegration.
Probabilistic Properties Of Deterministic Systems
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Author : Andrzej Lasota
language : en
Publisher: Cambridge University Press
Release Date : 2008-11-27
Probabilistic Properties Of Deterministic Systems written by Andrzej Lasota and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008-11-27 with Mathematics categories.
This book shows how densities arise in simple deterministic systems. There has been explosive growth in interest in physical, biological and economic systems that can be profitably studied using densities. Due to the inaccessibility of the mathematical literature there has been little diffusion of the applicable mathematics into the study of these 'chaotic' systems. This book will help to bridge that gap. The authors give a unified treatment of a variety of mathematical systems generating densities, ranging from one-dimensional discrete time transformations through continuous time systems described by integro-partial differential equations. They have drawn examples from many scientific fields to illustrate the utility of the techniques presented. The book assumes a knowledge of advanced calculus and differential equations, but basic concepts from measure theory, ergodic theory, the geometry of manifolds, partial differential equations, probability theory and Markov processes, and stochastic integrals and differential equations are introduced as needed.
Pseudo Differential Operators Markov Processes
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Author : Niels Jacob
language : en
Publisher: Imperial College Press
Release Date : 2005
Pseudo Differential Operators Markov Processes written by Niels Jacob and has been published by Imperial College Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2005 with Mathematics categories.
This volume concentrates on how to construct a Markov process by starting with a suitable pseudo-differential operator. Feller processes, Hunt processes associated with Lp-sub-Markovian semigroups and processes constructed by using the Martingale problem are at the center of the considerations. The potential theory of these processes is further developed and applications are discussed. Due to the non-locality of the generators, the processes are jump processes and their relations to Levy processes are investigated. Special emphasis is given to the symbol of a process, a notion which generalizes that of the characteristic exponent of a Levy process and provides a natural link to pseudo-differential operator theory.
Long Run Convergence In Greenhouse Gases Reactive Compounds Aerosol Precursors And Aerosols
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Author : Diego Romero-Ávila
language : en
Publisher: Springer Nature
Release Date : 2025-04-18
Long Run Convergence In Greenhouse Gases Reactive Compounds Aerosol Precursors And Aerosols written by Diego Romero-Ávila and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2025-04-18 with Business & Economics categories.
This book examines the presence of stochastic and deterministic convergence in ten series of greenhouse gases, aerosol precursors, and aerosols across 29 industrialized and emerging countries from 1820 to 2018. The author utilizes the Panel Analysis of Nonstationarity in Idiosyncratic and Common Components (PANIC) method for the empirical exercise. The analysis reveals strong evidence of stochastic convergence patterns in the series of log per capita emissions for black carbon, carbon monoxide, ammonia, non-methane volatile organic compounds, and nitrogen oxides, demonstrated by the existence of pairwise cointegration among individual series. Regarding deterministic convergence, the book provides compelling evidence of convergence in per capita emissions for black carbon, carbon monoxide, ammonia, non-methane volatile organic compounds, nitrogen oxides, and sulfur dioxide. There is also moderate evidence of convergence in per capita emissions for carbon dioxide, nitrous oxide, and organic carbon, and weaker evidence for methane emissions. The findings have significant implications for environmental policy, particularly in light of the observed deterministic convergence in emissions.
Numerical Solution Of Stochastic Differential Equations
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Author : Peter E. Kloeden
language : en
Publisher: Springer Science & Business Media
Release Date : 2011-06-15
Numerical Solution Of Stochastic Differential Equations written by Peter E. Kloeden and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-06-15 with Mathematics categories.
The numerical analysis of stochastic differential equations (SDEs) differs significantly from that of ordinary differential equations. This book provides an easily accessible introduction to SDEs, their applications and the numerical methods to solve such equations. From the reviews: "The authors draw upon their own research and experiences in obviously many disciplines... considerable time has obviously been spent writing this in the simplest language possible." --ZAMP
Robust Cluster Analysis And Variable Selection
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Author : Gunter Ritter
language : en
Publisher: CRC Press
Release Date : 2014-09-02
Robust Cluster Analysis And Variable Selection written by Gunter Ritter and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-09-02 with Computers categories.
Clustering remains a vibrant area of research in statistics. Although there are many books on this topic, there are relatively few that are well founded in the theoretical aspects. In Robust Cluster Analysis and Variable Selection, Gunter Ritter presents an overview of the theory and applications of probabilistic clustering and variable selection, synthesizing the key research results of the last 50 years. The author focuses on the robust clustering methods he found to be the most useful on simulated data and real-time applications. The book provides clear guidance for the varying needs of both applications, describing scenarios in which accuracy and speed are the primary goals. Robust Cluster Analysis and Variable Selection includes all of the important theoretical details, and covers the key probabilistic models, robustness issues, optimization algorithms, validation techniques, and variable selection methods. The book illustrates the different methods with simulated data and applies them to real-world data sets that can be easily downloaded from the web. This provides you with guidance in how to use clustering methods as well as applicable procedures and algorithms without having to understand their probabilistic fundamentals.
Chaos Fractals And Noise
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Author : Andrzej Lasota
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-11-27
Chaos Fractals And Noise written by Andrzej Lasota and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-11-27 with Mathematics categories.
The first edition of this book was originally published in 1985 under the ti tle "Probabilistic Properties of Deterministic Systems. " In the intervening years, interest in so-called "chaotic" systems has continued unabated but with a more thoughtful and sober eye toward applications, as befits a ma turing field. This interest in the serious usage of the concepts and techniques of nonlinear dynamics by applied scientists has probably been spurred more by the availability of inexpensive computers than by any other factor. Thus, computer experiments have been prominent, suggesting the wealth of phe nomena that may be resident in nonlinear systems. In particular, they allow one to observe the interdependence between the deterministic and probabilistic properties of these systems such as the existence of invariant measures and densities, statistical stability and periodicity, the influence of stochastic perturbations, the formation of attractors, and many others. The aim of the book, and especially of this second edition, is to present recent theoretical methods which allow one to study these effects. We have taken the opportunity in this second edition to not only correct the errors of the first edition, but also to add substantially new material in five sections and a new chapter.
Probability Random Variables And Random Processes
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Author : John J. Shynk
language : en
Publisher: John Wiley & Sons
Release Date : 2012-10-15
Probability Random Variables And Random Processes written by John J. Shynk and has been published by John Wiley & Sons this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-10-15 with Computers categories.
Probability, Random Variables, and Random Processes is a comprehensive textbook on probability theory for engineers that provides a more rigorous mathematical framework than is usually encountered in undergraduate courses. It is intended for first-year graduate students who have some familiarity with probability and random variables, though not necessarily of random processes and systems that operate on random signals. It is also appropriate for advanced undergraduate students who have a strong mathematical background. The book has the following features: Several appendices include related material on integration, important inequalities and identities, frequency-domain transforms, and linear algebra. These topics have been included so that the book is relatively self-contained. One appendix contains an extensive summary of 33 random variables and their properties such as moments, characteristic functions, and entropy. Unlike most books on probability, numerous figures have been included to clarify and expand upon important points. Over 600 illustrations and MATLAB plots have been designed to reinforce the material and illustrate the various characterizations and properties of random quantities. Sufficient statistics are covered in detail, as is their connection to parameter estimation techniques. These include classical Bayesian estimation and several optimality criteria: mean-square error, mean-absolute error, maximum likelihood, method of moments, and least squares. The last four chapters provide an introduction to several topics usually studied in subsequent engineering courses: communication systems and information theory; optimal filtering (Wiener and Kalman); adaptive filtering (FIR and IIR); and antenna beamforming, channel equalization, and direction finding. This material is available electronically at the companion website. Probability, Random Variables, and Random Processes is the only textbook on probability for engineers that includes relevant background material, provides extensive summaries of key results, and extends various statistical techniques to a range of applications in signal processing.