Students T Distribution And Related Stochastic Processes

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Student’s t-Distribution and Related Stochastic Processes

Author : Bronius Grigelionis
Publisher : Springer Science & Business Media
ISBN 13 : 3642311466
Total Pages : 105 pages
Book Rating : 4.6/5 (423 download)

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Book Synopsis Student’s t-Distribution and Related Stochastic Processes by : Bronius Grigelionis

Download or read book Student’s t-Distribution and Related Stochastic Processes written by Bronius Grigelionis and published by Springer Science & Business Media. This book was released on 2012-09-18 with total page 105 pages. Available in PDF, EPUB and Kindle. Book excerpt: This brief monograph is an in-depth study of the infinite divisibility and self-decomposability properties of central and noncentral Student’s distributions, represented as variance and mean-variance mixtures of multivariate Gaussian distributions with the reciprocal gamma mixing distribution. These results allow us to define and analyse Student-Lévy processes as Thorin subordinated Gaussian Lévy processes. A broad class of one-dimensional, strictly stationary diffusions with the Student’s t-marginal distribution are defined as the unique weak solution for the stochastic differential equation. Using the independently scattered random measures generated by the bi-variate centred Student-Lévy process, and stochastic integration theory, a univariate, strictly stationary process with the centred Student’s t- marginals and the arbitrary correlation structure are defined. As a promising direction for future work in constructing and analysing new multivariate Student-Lévy type processes, the notion of Lévy copulas and the related analogue of Sklar’s theorem are explained.

Normal and Student ́s t Distributions and Their Applications

Author : Mohammad Ahsanullah
Publisher : Springer Science & Business Media
ISBN 13 : 9462390614
Total Pages : 163 pages
Book Rating : 4.4/5 (623 download)

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Book Synopsis Normal and Student ́s t Distributions and Their Applications by : Mohammad Ahsanullah

Download or read book Normal and Student ́s t Distributions and Their Applications written by Mohammad Ahsanullah and published by Springer Science & Business Media. This book was released on 2014-02-07 with total page 163 pages. Available in PDF, EPUB and Kindle. Book excerpt: The most important properties of normal and Student t-distributions are presented. A number of applications of these properties are demonstrated. New related results dealing with the distributions of the sum, product and ratio of the independent normal and Student distributions are presented. The materials will be useful to the advanced undergraduate and graduate students and practitioners in the various fields of science and engineering.

Essentials of Stochastic Processes

Author : Richard Durrett
Publisher : Springer
ISBN 13 : 3319456148
Total Pages : 282 pages
Book Rating : 4.3/5 (194 download)

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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.

Generalized Gamma Convolutions and Related Classes of Distributions and Densities

Author : Lennart Bondesson
Publisher : Springer Science & Business Media
ISBN 13 : 1461229480
Total Pages : 184 pages
Book Rating : 4.4/5 (612 download)

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Book Synopsis Generalized Gamma Convolutions and Related Classes of Distributions and Densities by : Lennart Bondesson

Download or read book Generalized Gamma Convolutions and Related Classes of Distributions and Densities written by Lennart Bondesson and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 184 pages. Available in PDF, EPUB and Kindle. Book excerpt: Generalized Gamma convolutions were introduced by Olof Thorin in 1977 and were used by him to show that, in particular, the Lognormal distribution is infinitely divisible. After that a large number of papers rapidly appeared with new results in a somewhat random order. Many of the papers appeared in the Scandinavian Actuarial Journal. This work is an attempt to present the main results on this class of probability distributions and related classes in a rather logical order. The goal has been to be on a level that is not too advanced. However, since the field is rather technical, most readers will find difficult passages in the text. Those who do not want to visit a mysterious land situated between the land of probability theory and statistics and the land of classical analysis should not look at this work. When some years ago I submitted a survey to a journal it was suggested by the editor, K. Krickeberg, that it should be expanded to a book. However, at that time I was rather reluctant to do so since there remained so many problems to be solved or to be solved in a smoother way than before. Moreover, there was at that time some lack of probabilistic interpretations and applications. Many of the problems are now solved but still it is felt that more applications than those presented in the work could be found.

Stochastic Methods in Engineering

Author : I. St Doltsinis
Publisher : WIT Press
ISBN 13 : 1845646266
Total Pages : 379 pages
Book Rating : 4.8/5 (456 download)

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Book Synopsis Stochastic Methods in Engineering by : I. St Doltsinis

Download or read book Stochastic Methods in Engineering written by I. St Doltsinis and published by WIT Press. This book was released on 2012 with total page 379 pages. Available in PDF, EPUB and Kindle. Book excerpt: The increasing industrial demand for reliable quantification and management of uncertainty in product performance forces engineers to employ probabilistic models in analysis and design, a fact that has occasioned considerable research and development activities in the field. Notes on Stochastics eventually address the topic of computational stochastic mechanics. The single volume uniquely presents tutorials on essential probabilistics and statistics, recent finite element methods for stochastic analysis by Taylor series expansion as well as Monte Carlo simulation techniques. Design improvement and robust optimisation represent key issues as does reliability assessment. The subject is developed for solids and structures of elastic and elasto-plastic material, large displacements and material deformation processes; principles are transferable to various disciplines. A chapter is devoted to the statistical comparison of systems exhibiting random scatter. Where appropriate examples illustrate the theory, problems to solve appear instructive; applications are presented with relevance to engineering practice. The book, emanating from a university course, includes research and development in the field of computational stochastic analysis and optimization. It is intended for advanced students in engineering and for professionals who wish to extend their knowledge and skills in computational mechanics to the domain of stochastics. Contents: Introduction, Randomness, Structural analysis by Taylor series expansion, Design optimization, Robustness, Monte Carlo techniques for system response and design improvement, Reliability, Time variant phenomena, Material deformation processes, Analysis and comparison of data sets, Probability distribution of test functions.

Convergence of Stochastic Processes

Author : D. Pollard
Publisher : David Pollard
ISBN 13 : 0387909907
Total Pages : 223 pages
Book Rating : 4.3/5 (879 download)

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Book Synopsis Convergence of Stochastic Processes by : D. Pollard

Download or read book Convergence of Stochastic Processes written by D. Pollard and published by David Pollard. This book was released on 1984-10-08 with total page 223 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Probability, Statistics, and Stochastic Processes for Engineers and Scientists

Author : Aliakbar Montazer Haghighi
Publisher : CRC Press
ISBN 13 : 1351238396
Total Pages : 635 pages
Book Rating : 4.3/5 (512 download)

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Book Synopsis Probability, Statistics, and Stochastic Processes for Engineers and Scientists by : Aliakbar Montazer Haghighi

Download or read book Probability, Statistics, and Stochastic Processes for Engineers and Scientists written by Aliakbar Montazer Haghighi and published by CRC Press. This book was released on 2020-07-14 with total page 635 pages. Available in PDF, EPUB and Kindle. Book excerpt: 2020 Taylor & Francis Award Winner for Outstanding New Textbook! Featuring recent advances in the field, this new textbook presents probability and statistics, and their applications in stochastic processes. This book presents key information for understanding the essential aspects of basic probability theory and concepts of reliability as an application. The purpose of this book is to provide an option in this field that combines these areas in one book, balances both theory and practical applications, and also keeps the practitioners in mind. Features Includes numerous examples using current technologies with applications in various fields of study Offers many practical applications of probability in queueing models, all of which are related to the appropriate stochastic processes (continuous time such as waiting time, and fuzzy and discrete time like the classic Gambler’s Ruin Problem) Presents different current topics like probability distributions used in real-world applications of statistics such as climate control and pollution Different types of computer software such as MATLAB®, Minitab, MS Excel, and R as options for illustration, programing and calculation purposes and data analysis Covers reliability and its application in network queues

An Introduction to Stochastic Modeling

Author : Howard M. Taylor
Publisher : Academic Press
ISBN 13 : 1483269272
Total Pages : 410 pages
Book Rating : 4.4/5 (832 download)

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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.

Probability, Statistics, and Stochastic Processes

Author : Peter Olofsson
Publisher : John Wiley & Sons
ISBN 13 : 0470889748
Total Pages : 573 pages
Book Rating : 4.4/5 (78 download)

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Book Synopsis Probability, Statistics, and Stochastic Processes by : Peter Olofsson

Download or read book Probability, Statistics, and Stochastic Processes written by Peter Olofsson and published by John Wiley & Sons. This book was released on 2012-05-22 with total page 573 pages. Available in PDF, EPUB and Kindle. Book excerpt: Praise for the First Edition ". . . an excellent textbook . . . well organized and neatly written." —Mathematical Reviews ". . . amazingly interesting . . ." —Technometrics Thoroughly updated to showcase the interrelationships between probability, statistics, and stochastic processes, Probability, Statistics, and Stochastic Processes, Second Edition prepares readers to collect, analyze, and characterize data in their chosen fields. Beginning with three chapters that develop probability theory and introduce the axioms of probability, random variables, and joint distributions, the book goes on to present limit theorems and simulation. The authors combine a rigorous, calculus-based development of theory with an intuitive approach that appeals to readers' sense of reason and logic. Including more than 400 examples that help illustrate concepts and theory, the Second Edition features new material on statistical inference and a wealth of newly added topics, including: Consistency of point estimators Large sample theory Bootstrap simulation Multiple hypothesis testing Fisher's exact test and Kolmogorov-Smirnov test Martingales, renewal processes, and Brownian motion One-way analysis of variance and the general linear model Extensively class-tested to ensure an accessible presentation, Probability, Statistics, and Stochastic Processes, Second Edition is an excellent book for courses on probability and statistics at the upper-undergraduate level. The book is also an ideal resource for scientists and engineers in the fields of statistics, mathematics, industrial management, and engineering.

Combinatorial Stochastic Processes

Author : Jim Pitman
Publisher : Springer Science & Business Media
ISBN 13 : 354030990X
Total Pages : 257 pages
Book Rating : 4.5/5 (43 download)

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Book Synopsis Combinatorial Stochastic Processes by : Jim Pitman

Download or read book Combinatorial Stochastic Processes written by Jim Pitman and published by Springer Science & Business Media. This book was released on 2006-05-11 with total page 257 pages. Available in PDF, EPUB and Kindle. Book excerpt: The purpose of this text is to bring graduate students specializing in probability theory to current research topics at the interface of combinatorics and stochastic processes. There is particular focus on the theory of random combinatorial structures such as partitions, permutations, trees, forests, and mappings, and connections between the asymptotic theory of enumeration of such structures and the theory of stochastic processes like Brownian motion and Poisson processes.

Stationary and Related Stochastic Processes

Author : Harald Cramér
Publisher : Courier Corporation
ISBN 13 : 0486153355
Total Pages : 368 pages
Book Rating : 4.4/5 (861 download)

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Book Synopsis Stationary and Related Stochastic Processes by : Harald Cramér

Download or read book Stationary and Related Stochastic Processes written by Harald Cramér and published by Courier Corporation. This book was released on 2013-01-15 with total page 368 pages. Available in PDF, EPUB and Kindle. Book excerpt: This graduate-level text offers a comprehensive account of the general theory of stationary processes and develops the foundations of the general theory of stochastic processes, examines processes with a continuous-time parameter, more. 1967 edition.

Conditional Specification of Statistical Models

Author : Barry C. Arnold
Publisher : Springer Science & Business Media
ISBN 13 : 0387225889
Total Pages : 419 pages
Book Rating : 4.3/5 (872 download)

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Book Synopsis Conditional Specification of Statistical Models by : Barry C. Arnold

Download or read book Conditional Specification of Statistical Models written by Barry C. Arnold and published by Springer Science & Business Media. This book was released on 2007-06-02 with total page 419 pages. Available in PDF, EPUB and Kindle. Book excerpt: Efforts to visualize multivariate densities necessarily involve the use of cross-sections, or, equivalently, conditional densities. This book focuses on distributions that are completely specified in terms of conditional densities. They are appropriately used in any modeling situation where conditional information is completely or partially available. All statistical researchers seeking more flexible models than those provided by classical models will find conditionally specified distributions of interest.

Stochastic Processes and Applications

Author : Grigorios A. Pavliotis
Publisher : Springer
ISBN 13 : 1493913239
Total Pages : 345 pages
Book Rating : 4.4/5 (939 download)

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Book Synopsis Stochastic Processes and Applications by : Grigorios A. Pavliotis

Download or read book Stochastic Processes and Applications written by Grigorios A. Pavliotis and published by Springer. This book was released on 2014-11-19 with total page 345 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents various results and techniques from the theory of stochastic processes that are useful in the study of stochastic problems in the natural sciences. The main focus is analytical methods, although numerical methods and statistical inference methodologies for studying diffusion processes are also presented. The goal is the development of techniques that are applicable to a wide variety of stochastic models that appear in physics, chemistry and other natural sciences. Applications such as stochastic resonance, Brownian motion in periodic potentials and Brownian motors are studied and the connection between diffusion processes and time-dependent statistical mechanics is elucidated. The book contains a large number of illustrations, examples, and exercises. It will be useful for graduate-level courses on stochastic processes for students in applied mathematics, physics and engineering. Many of the topics covered in this book (reversible diffusions, convergence to equilibrium for diffusion processes, inference methods for stochastic differential equations, derivation of the generalized Langevin equation, exit time problems) cannot be easily found in textbook form and will be useful to both researchers and students interested in the applications of stochastic processes.

Probability and Stochastic Processes

Author : Ionut Florescu
Publisher : John Wiley & Sons
ISBN 13 : 1118593138
Total Pages : 578 pages
Book Rating : 4.1/5 (185 download)

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Book Synopsis Probability and Stochastic Processes by : Ionut Florescu

Download or read book Probability and Stochastic Processes written by Ionut Florescu and published by John Wiley & Sons. This book was released on 2014-12-04 with total page 578 pages. Available in PDF, EPUB and Kindle. Book excerpt: A comprehensive and accessible presentation of probability and stochastic processes with emphasis on key theoretical concepts and real-world applications With a sophisticated approach, Probability and Stochastic Processes successfully balances theory and applications in a pedagogical and accessible format. The book’s primary focus is on key theoretical notions in probability to provide a foundation for understanding concepts and examples related to stochastic processes. Organized into two main sections, the book begins by developing probability theory with topical coverage on probability measure; random variables; integration theory; product spaces, conditional distribution, and conditional expectations; and limit theorems. The second part explores stochastic processes and related concepts including the Poisson process, renewal processes, Markov chains, semi-Markov processes, martingales, and Brownian motion. Featuring a logical combination of traditional and complex theories as well as practices, Probability and Stochastic Processes also includes: Multiple examples from disciplines such as business, mathematical finance, and engineering Chapter-by-chapter exercises and examples to allow readers to test their comprehension of the presented material A rigorous treatment of all probability and stochastic processes concepts An appropriate textbook for probability and stochastic processes courses at the upper-undergraduate and graduate level in mathematics, business, and electrical engineering, Probability and Stochastic Processes is also an ideal reference for researchers and practitioners in the fields of mathematics, engineering, and finance.

Stochastic-Process Limits

Author : Ward Whitt
Publisher : Springer Science & Business Media
ISBN 13 : 0387217487
Total Pages : 616 pages
Book Rating : 4.3/5 (872 download)

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Book Synopsis Stochastic-Process Limits by : Ward Whitt

Download or read book Stochastic-Process Limits written by Ward Whitt and published by Springer Science & Business Media. This book was released on 2006-04-11 with total page 616 pages. Available in PDF, EPUB and Kindle. Book excerpt: From the reviews: "The material is self-contained, but it is technical and a solid foundation in probability and queuing theory is beneficial to prospective readers. [... It] is intended to be accessible to those with less background. This book is a must to researchers and graduate students interested in these areas." ISI Short Book Reviews

Wireless, Networking, Radar, Sensor Array Processing, and Nonlinear Signal Processing

Author : Vijay Madisetti
Publisher : CRC Press
ISBN 13 : 1420046055
Total Pages : 874 pages
Book Rating : 4.4/5 (2 download)

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Book Synopsis Wireless, Networking, Radar, Sensor Array Processing, and Nonlinear Signal Processing by : Vijay Madisetti

Download or read book Wireless, Networking, Radar, Sensor Array Processing, and Nonlinear Signal Processing written by Vijay Madisetti and published by CRC Press. This book was released on 2018-09-03 with total page 874 pages. Available in PDF, EPUB and Kindle. Book excerpt: Now available in a three-volume set, this updated and expanded edition of the bestselling The Digital Signal Processing Handbook continues to provide the engineering community with authoritative coverage of the fundamental and specialized aspects of information-bearing signals in digital form. Encompassing essential background material, technical details, standards, and software, the second edition reflects cutting-edge information on signal processing algorithms and protocols related to speech, audio, multimedia, and video processing technology associated with standards ranging from WiMax to MP3 audio, low-power/high-performance DSPs, color image processing, and chips on video. Drawing on the experience of leading engineers, researchers, and scholars, the three-volume set contains 29 new chapters that address multimedia and Internet technologies, tomography, radar systems, architecture, standards, and future applications in speech, acoustics, video, radar, and telecommunications. This volume, Wireless, Networking, Radar, Sensor Array Processing, and Nonlinear Signal Processing, provides complete coverage of the foundations of signal processing related to wireless, radar, space–time coding, and mobile communications, together with associated applications to networking, storage, and communications.

Introduction to Probability and Stochastic Processes with Applications

Author : Liliana Blanco Castañeda
Publisher : John Wiley & Sons
ISBN 13 : 1118344960
Total Pages : 613 pages
Book Rating : 4.1/5 (183 download)

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Book Synopsis Introduction to Probability and Stochastic Processes with Applications by : Liliana Blanco Castañeda

Download or read book Introduction to Probability and Stochastic Processes with Applications written by Liliana Blanco Castañeda and published by John Wiley & Sons. This book was released on 2014-08-21 with total page 613 pages. Available in PDF, EPUB and Kindle. Book excerpt: An easily accessible, real-world approach to probability and stochastic processes Introduction to Probability and Stochastic Processes with Applications presents a clear, easy-to-understand treatment of probability and stochastic processes, providing readers with a solid foundation they can build upon throughout their careers. With an emphasis on applications in engineering, applied sciences, business and finance, statistics, mathematics, and operations research, the book features numerous real-world examples that illustrate how random phenomena occur in nature and how to use probabilistic techniques to accurately model these phenomena. The authors discuss a broad range of topics, from the basic concepts of probability to advanced topics for further study, including Itô integrals, martingales, and sigma algebras. Additional topical coverage includes: Distributions of discrete and continuous random variables frequently used in applications Random vectors, conditional probability, expectation, and multivariate normal distributions The laws of large numbers, limit theorems, and convergence of sequences of random variables Stochastic processes and related applications, particularly in queueing systems Financial mathematics, including pricing methods such as risk-neutral valuation and the Black-Scholes formula Extensive appendices containing a review of the requisite mathematics and tables of standard distributions for use in applications are provided, and plentiful exercises, problems, and solutions are found throughout. Also, a related website features additional exercises with solutions and supplementary material for classroom use. Introduction to Probability and Stochastic Processes with Applications is an ideal book for probability courses at the upper-undergraduate level. The book is also a valuable reference for researchers and practitioners in the fields of engineering, operations research, and computer science who conduct data analysis to make decisions in their everyday work.