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Fundamentals Of The Theory Of Structured Dependence Between Stochastic Processes
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Book Synopsis Fundamentals of the Theory of Structured Dependence between Stochastic Processes by : Tomasz R. Bielecki
Download or read book Fundamentals of the Theory of Structured Dependence between Stochastic Processes written by Tomasz R. Bielecki and published by Cambridge University Press. This book was released on 2020-08-27 with total page 279 pages. Available in PDF, EPUB and Kindle. Book excerpt: Comprehensive presentation of the technical aspects and applications of the theory of structured dependence between random processes.
Book Synopsis Foundations of Constructive Probability Theory by : Yuen-Kwok Chan
Download or read book Foundations of Constructive Probability Theory written by Yuen-Kwok Chan and published by Cambridge University Press. This book was released on 2021-05-27 with total page 627 pages. Available in PDF, EPUB and Kindle. Book excerpt: Using Bishop's work on constructive analysis as a framework, this monograph gives a systematic, detailed and general constructive theory of probability theory and stochastic processes. It is the first extended account of this theory: almost all of the constructive existence and continuity theorems that permeate the book are original. It also contains results and methods hitherto unknown in the constructive and nonconstructive settings. The text features logic only in the common sense and, beyond a certain mathematical maturity, requires no prior training in either constructive mathematics or probability theory. It will thus be accessible and of interest, both to probabilists interested in the foundations of their speciality and to constructive mathematicians who wish to see Bishop's theory applied to a particular field.
Book Synopsis Asymptotic Analysis of Random Walks by : A. A. Borovkov
Download or read book Asymptotic Analysis of Random Walks written by A. A. Borovkov and published by Cambridge University Press. This book was released on 2020-10-29 with total page 437 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is a companion book to Asymptotic Analysis of Random Walks: Heavy-Tailed Distributions by A.A. Borovkov and K.A. Borovkov. Its self-contained systematic exposition provides a highly useful resource for academic researchers and professionals interested in applications of probability in statistics, ruin theory, and queuing theory. The large deviation principle for random walks was first established by the author in 1967, under the restrictive condition that the distribution tails decay faster than exponentially. (A close assertion was proved by S.R.S. Varadhan in 1966, but only in a rather special case.) Since then, the principle has always been treated in the literature only under this condition. Recently, the author jointly with A.A. Mogul'skii removed this restriction, finding a natural metric for which the large deviation principle for random walks holds without any conditions. This new version is presented in the book, as well as a new approach to studying large deviations in boundary crossing problems. Many results presented in the book, obtained by the author himself or jointly with co-authors, are appearing in a monograph for the first time.
Book Synopsis Asymptotic Analysis of Random Walks: Light-Tailed Distributions by : A.A. Borovkov
Download or read book Asymptotic Analysis of Random Walks: Light-Tailed Distributions written by A.A. Borovkov and published by Cambridge University Press. This book was released on 2020-10-29 with total page 437 pages. Available in PDF, EPUB and Kindle. Book excerpt: A systematic modern treatise on large deviation theory for random walks with light tails, from one of its key creators.
Book Synopsis Fundamentals of Decision Making and Priority Theory With the Analytic Hierarchy Process by : Thomas L. Saaty
Download or read book Fundamentals of Decision Making and Priority Theory With the Analytic Hierarchy Process written by Thomas L. Saaty and published by RWS Publications. This book was released on with total page 424 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is a comprehensive summary, primarily of the author's own thinking and research, about the Analytic Hierarchy Process and decision making. It includes advanced mathematical theory and diverse applications. Fundamentals of Decision Making has all the latest theoretical developments in the AHP and new theoretical material not published elsewhere. We consider this book to be the replacement for the original book on the subject, The Analytic Hierarchy Process that was published by McGraw Hill Publishers, New York.
Book Synopsis Essentials of Stochastic Processes by : Richard Durrett
Download or read book Essentials of Stochastic Processes written by Richard Durrett and published by Springer. This book was released on 2016-11-07 with total page 282 pages. Available in PDF, EPUB and Kindle. Book excerpt: Building upon the previous editions, this textbook is a first course in stochastic processes taken by undergraduate and graduate students (MS and PhD students from math, statistics, economics, computer science, engineering, and finance departments) who have had a course in probability theory. It covers Markov chains in discrete and continuous time, Poisson processes, renewal processes, martingales, and option pricing. One can only learn a subject by seeing it in action, so there are a large number of examples and more than 300 carefully chosen exercises to deepen the reader’s understanding. Drawing from teaching experience and student feedback, there are many new examples and problems with solutions that use TI-83 to eliminate the tedious details of solving linear equations by hand, and the collection of exercises is much improved, with many more biological examples. Originally included in previous editions, material too advanced for this first course in stochastic processes has been eliminated while treatment of other topics useful for applications has been expanded. In addition, the ordering of topics has been improved; for example, the difficult subject of martingales is delayed until its usefulness can be applied in the treatment of mathematical finance.
Book Synopsis Basics of Applied Stochastic Processes by : Richard Serfozo
Download or read book Basics of Applied Stochastic Processes written by Richard Serfozo and published by Springer Science & Business Media. This book was released on 2009-01-24 with total page 452 pages. Available in PDF, EPUB and Kindle. Book excerpt: Stochastic processes are mathematical models of random phenomena that evolve according to prescribed dynamics. Processes commonly used in applications are Markov chains in discrete and continuous time, renewal and regenerative processes, Poisson processes, and Brownian motion. This volume gives an in-depth description of the structure and basic properties of these stochastic processes. A main focus is on equilibrium distributions, strong laws of large numbers, and ordinary and functional central limit theorems for cost and performance parameters. Although these results differ for various processes, they have a common trait of being limit theorems for processes with regenerative increments. Extensive examples and exercises show how to formulate stochastic models of systems as functions of a system’s data and dynamics, and how to represent and analyze cost and performance measures. Topics include stochastic networks, spatial and space-time Poisson processes, queueing, reversible processes, simulation, Brownian approximations, and varied Markovian models. The technical level of the volume is between that of introductory texts that focus on highlights of applied stochastic processes, and advanced texts that focus on theoretical aspects of processes.
Book Synopsis Multiscale Analysis of Complex Time Series by : Jianbo Gao
Download or read book Multiscale Analysis of Complex Time Series written by Jianbo Gao and published by John Wiley & Sons. This book was released on 2007-12-04 with total page 368 pages. Available in PDF, EPUB and Kindle. Book excerpt: The only integrative approach to chaos and random fractal theory Chaos and random fractal theory are two of the most important theories developed for data analysis. Until now, there has been no single book that encompasses all of the basic concepts necessary for researchers to fully understand the ever-expanding literature and apply novel methods to effectively solve their signal processing problems. Multiscale Analysis of Complex Time Series fills this pressing need by presenting chaos and random fractal theory in a unified manner. Adopting a data-driven approach, the book covers: DNA sequence analysis EEG analysis Heart rate variability analysis Neural information processing Network traffic modeling Economic time series analysis And more Additionally, the book illustrates almost every concept presented through applications and a dedicated Web site is available with source codes written in various languages, including Java, Fortran, C, and MATLAB, together with some simulated and experimental data. The only modern treatment of signal processing with chaos and random fractals unified, this is an essential book for researchers and graduate students in electrical engineering, computer science, bioengineering, and many other fields.
Book Synopsis Theory and Applications of Long-Range Dependence by : Paul Doukhan
Download or read book Theory and Applications of Long-Range Dependence written by Paul Doukhan and published by Springer Science & Business Media. This book was released on 2002-12-13 with total page 744 pages. Available in PDF, EPUB and Kindle. Book excerpt: The area of data analysis has been greatly affected by our computer age. For example, the issue of collecting and storing huge data sets has become quite simplified and has greatly affected such areas as finance and telecommunications. Even non-specialists try to analyze data sets and ask basic questions about their structure. One such question is whether one observes some type of invariance with respect to scale, a question that is closely related to the existence of long-range dependence in the data. This important topic of long-range dependence is the focus of this unique work, written by a number of specialists on the subject. The topics selected should give a good overview from the probabilistic and statistical perspective. Included will be articles on fractional Brownian motion, models, inequalities and limit theorems, periodic long-range dependence, parametric, semiparametric, and non-parametric estimation, long-memory stochastic volatility models, robust estimation, and prediction for long-range dependence sequences. For those graduate students and researchers who want to use the methodology and need to know the "tricks of the trade," there will be a special section called "Mathematical Techniques." Topics in the first part of the book are covered from probabilistic and statistical perspectives and include fractional Brownian motion, models, inequalities and limit theorems, periodic long-range dependence, parametric, semiparametric, and non-parametric estimation, long-memory stochastic volatility models, robust estimation, prediction for long-range dependence sequences. The reader is referred to more detailed proofs if already found in the literature. The last part of the book is devoted to applications in the areas of simulation, estimation and wavelet techniques, traffic in computer networks, econometry and finance, multifractal models, and hydrology. Diagrams and illustrations enhance the presentation. Each article begins with introductory background material and is accessible to mathematicians, a variety of practitioners, and graduate students. The work serves as a state-of-the art reference or graduate seminar text.
Book Synopsis Time-Dependent Reliability Theory and Its Applications by : Chun-Qing Li
Download or read book Time-Dependent Reliability Theory and Its Applications written by Chun-Qing Li and published by Elsevier. This book was released on 2022-10-28 with total page 626 pages. Available in PDF, EPUB and Kindle. Book excerpt: Time-Dependent Reliability Theory and Its Applications introduces the theory of time-dependent reliability and presents methods to determine the reliability of structures over the lifespan of their services. The book contains state-of-the-art solutions to first passage probability derived from the theory of stochastic processes with different types of probability distribution functions, including Gaussian and non-Gaussian distributions and stationary and non-stationary processes. In addition, it provides various methods to determine the probability of failure over time, considering different failure modes and a methodology to predict the service life of structures. Sections also cover the applications of time-dependent reliability to prediction of service life and development of risk cost-optimized maintenance strategy for existing structures. This new book is for those who wants to know how to predict the service life of a structure (buildings, bridges, aircraft structures, etc.) and how to develop a risk-cost, optimized maintenance strategy for these structures. Presents the basic knowledge required to predict service life and develop a maintenance strategy for infrastructure Explains how to predict the remaining safe life of the infrastructure during its lifespan of operation Describes how to carry out maintenance for an infrastructure to ensure its safe and serviceable operation during the designed service life
Book Synopsis Long Range Dependence by : Gennady Samorodnitsky
Download or read book Long Range Dependence written by Gennady Samorodnitsky and published by Now Publishers Inc. This book was released on 2007 with total page 109 pages. Available in PDF, EPUB and Kindle. Book excerpt: Long Range Dependence is a wide ranging survey of the ideas, models and techniques associated with the notion of long memory. It will serve as an invaluable reference source for researchers studying long range dependence, for those building long memory models, and for people who are trying to detect the possible presence of long memory in data.
Book Synopsis Empirical Process Techniques for Dependent Data by : Herold Dehling
Download or read book Empirical Process Techniques for Dependent Data written by Herold Dehling and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 378 pages. Available in PDF, EPUB and Kindle. Book excerpt: Empirical process techniques for independent data have been used for many years in statistics and probability theory. These techniques have proved very useful for studying asymptotic properties of parametric as well as non-parametric statistical procedures. Recently, the need to model the dependence structure in data sets from many different subject areas such as finance, insurance, and telecommunications has led to new developments concerning the empirical distribution function and the empirical process for dependent, mostly stationary sequences. This work gives an introduction to this new theory of empirical process techniques, which has so far been scattered in the statistical and probabilistic literature, and surveys the most recent developments in various related fields. Key features: A thorough and comprehensive introduction to the existing theory of empirical process techniques for dependent data * Accessible surveys by leading experts of the most recent developments in various related fields * Examines empirical process techniques for dependent data, useful for studying parametric and non-parametric statistical procedures * Comprehensive bibliographies * An overview of applications in various fields related to empirical processes: e.g., spectral analysis of time-series, the bootstrap for stationary sequences, extreme value theory, and the empirical process for mixing dependent observations, including the case of strong dependence. To date this book is the only comprehensive treatment of the topic in book literature. It is an ideal introductory text that will serve as a reference or resource for classroom use in the areas of statistics, time-series analysis, extreme value theory, point process theory, and applied probability theory. Contributors: P. Ango Nze, M.A. Arcones, I. Berkes, R. Dahlhaus, J. Dedecker, H.G. Dehling,
Book Synopsis Mathematical Principles of the Internet, Volume 1 by : Nirdosh Bhatnagar
Download or read book Mathematical Principles of the Internet, Volume 1 written by Nirdosh Bhatnagar and published by CRC Press. This book was released on 2018-11-20 with total page 780 pages. Available in PDF, EPUB and Kindle. Book excerpt: This two-volume set on Mathematical Principles of the Internet provides a comprehensive overview of the mathematical principles of Internet engineering. The books do not aim to provide all of the mathematical foundations upon which the Internet is based. Instead, they cover a partial panorama and the key principles. Volume 1 explores Internet engineering, while the supporting mathematics is covered in Volume 2. The chapters on mathematics complement those on the engineering episodes, and an effort has been made to make this work succinct, yet self-contained. Elements of information theory, algebraic coding theory, cryptography, Internet traffic, dynamics and control of Internet congestion, and queueing theory are discussed. In addition, stochastic networks, graph-theoretic algorithms, application of game theory to the Internet, Internet economics, data mining and knowledge discovery, and quantum computation, communication, and cryptography are also discussed. In order to study the structure and function of the Internet, only a basic knowledge of number theory, abstract algebra, matrices and determinants, graph theory, geometry, analysis, optimization theory, probability theory, and stochastic processes, is required. These mathematical disciplines are defined and developed in the books to the extent that is needed to develop and justify their application to Internet engineering.
Book Synopsis An Introduction to Stochastic Modeling by : Howard M. Taylor
Download or read book An Introduction to Stochastic Modeling written by Howard M. Taylor and published by Academic Press. This book was released on 2014-05-10 with total page 410 pages. Available in PDF, EPUB and Kindle. Book excerpt: An Introduction to Stochastic Modeling provides information pertinent to the standard concepts and methods of stochastic modeling. This book presents the rich diversity of applications of stochastic processes in the sciences. Organized into nine chapters, this book begins with an overview of diverse types of stochastic models, which predicts a set of possible outcomes weighed by their likelihoods or probabilities. This text then provides exercises in the applications of simple stochastic analysis to appropriate problems. Other chapters consider the study of general functions of independent, identically distributed, nonnegative random variables representing the successive intervals between renewals. This book discusses as well the numerous examples of Markov branching processes that arise naturally in various scientific disciplines. The final chapter deals with queueing models, which aid the design process by predicting system performance. This book is a valuable resource for students of engineering and management science. Engineers will also find this book useful.
Book Synopsis Basics of Probability and Stochastic Processes by : Esra Bas
Download or read book Basics of Probability and Stochastic Processes written by Esra Bas and published by Springer Nature. This book was released on 2019-11-05 with total page 307 pages. Available in PDF, EPUB and Kindle. Book excerpt: This textbook explores probability and stochastic processes at a level that does not require any prior knowledge except basic calculus. It presents the fundamental concepts in a step-by-step manner, and offers remarks and warnings for deeper insights. The chapters include basic examples, which are revisited as the new concepts are introduced. To aid learning, figures and diagrams are used to help readers grasp the concepts, and the solutions to the exercises and problems. Further, a table format is also used where relevant for better comparison of the ideas and formulae. The first part of the book introduces readers to the essentials of probability, including combinatorial analysis, conditional probability, and discrete and continuous random variable. The second part then covers fundamental stochastic processes, including point, counting, renewal and regenerative processes, the Poisson process, Markov chains, queuing models and reliability theory. Primarily intended for undergraduate engineering students, it is also useful for graduate-level students wanting to refresh their knowledge of the basics of probability and stochastic processes.
Book Synopsis Statistical Analysis of Stochastic Processes in Time by : J. K. Lindsey
Download or read book Statistical Analysis of Stochastic Processes in Time written by J. K. Lindsey and published by Cambridge University Press. This book was released on 2004-08-02 with total page 356 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book was first published in 2004. Many observed phenomena, from the changing health of a patient to values on the stock market, are characterised by quantities that vary over time: stochastic processes are designed to study them. This book introduces practical methods of applying stochastic processes to an audience knowledgeable only in basic statistics. It covers almost all aspects of the subject and presents the theory in an easily accessible form that is highlighted by application to many examples. These examples arise from dozens of areas, from sociology through medicine to engineering. Complementing these are exercise sets making the book suited for introductory courses in stochastic processes. Software (available from www.cambridge.org) is provided for the freely available R system for the reader to apply to all the models presented.
Book Synopsis Copula Theory and Its Applications by : Piotr Jaworski
Download or read book Copula Theory and Its Applications written by Piotr Jaworski and published by Springer Science & Business Media. This book was released on 2010-07-16 with total page 338 pages. Available in PDF, EPUB and Kindle. Book excerpt: Copulas are mathematical objects that fully capture the dependence structure among random variables and hence offer great flexibility in building multivariate stochastic models. Since their introduction in the early 50's, copulas have gained considerable popularity in several fields of applied mathematics, such as finance, insurance and reliability theory. Today, they represent a well-recognized tool for market and credit models, aggregation of risks, portfolio selection, etc. This book is divided into two main parts: Part I - "Surveys" contains 11 chapters that provide an up-to-date account of essential aspects of copula models. Part II - "Contributions" collects the extended versions of 6 talks selected from papers presented at the workshop in Warsaw.
