Stochastic Processes

Theory for Applications
Author: Robert G. Gallager
Publisher: Cambridge University Press
ISBN: 1107435315
Category: Technology & Engineering
Page: 568
View: 5415

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This definitive textbook provides a solid introduction to discrete and continuous stochastic processes, tackling a complex field in a way that instils a deep understanding of the relevant mathematical principles, and develops an intuitive grasp of the way these principles can be applied to modelling real-world systems. It includes a careful review of elementary probability and detailed coverage of Poisson, Gaussian and Markov processes with richly varied queuing applications. The theory and applications of inference, hypothesis testing, estimation, random walks, large deviations, martingales and investments are developed. Written by one of the world's leading information theorists, evolving over twenty years of graduate classroom teaching and enriched by over 300 exercises, this is an exceptional resource for anyone looking to develop their understanding of stochastic processes.

Stationary Stochastic Processes

Theory and Applications
Author: Georg Lindgren
Publisher: CRC Press
ISBN: 1466557796
Category: Mathematics
Page: 375
View: 1447

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Intended for a second course in stationary processes, Stationary Stochastic Processes: Theory and Applications presents the theory behind the field’s widely scattered applications in engineering and science. In addition, it reviews sample function properties and spectral representations for stationary processes and fields, including a portion on stationary point processes. Features Presents and illustrates the fundamental correlation and spectral methods for stochastic processes and random fields Explains how the basic theory is used in special applications like detection theory and signal processing, spatial statistics, and reliability Motivates mathematical theory from a statistical model-building viewpoint Introduces a selection of special topics, including extreme value theory, filter theory, long-range dependence, and point processes Provides more than 100 exercises with hints to solutions and selected full solutions This book covers key topics such as ergodicity, crossing problems, and extremes, and opens the doors to a selection of special topics, like extreme value theory, filter theory, long-range dependence, and point processes, and includes many exercises and examples to illustrate the theory. Precise in mathematical details without being pedantic, Stationary Stochastic Processes: Theory and Applications is for the student with some experience with stochastic processes and a desire for deeper understanding without getting bogged down in abstract mathematics.

Verallgemeinerte stochastische Prozesse

Modellierung und Anwendung technischer Rauschprozesse
Author: Stefan Schäffler
Publisher: Springer-Verlag
ISBN: 366254265X
Category: Mathematics
Page: 183
View: 1006

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Dieses Lehrbuch behandelt die in Natur- und Ingenieurwissenschaften eine zentrale Rolle spielenden Rauschprozesse, wie weißes Rauschen in der Raumsondenkommunikation oder thermisches Rauschen und Schrotrauschen in elektronischen Bauelementen.In dieser Form einzigartig, entwickelt der Autor die mathematische Theorie der verallgemeinerten stochastischen Prozesse und spricht dabei die Anwendung dieser mathematischen Objekte in der Praxis (z.B. Schaltkreissimulation, digitale Nachrichtenübertragung und Bildverarbeitung) an; somit dient dieses Lehrbuch auch als praxisrelevante Einführung in die Modellierung und Verwendung technischer Rauschprozesse. Die mathematische Modellierung von Rauschprozessen führt auf die Theorie stochastischer Prozesse auf Basis verallgemeinerter Funktionen (Distributionen), ohne die kein Handy funktionieren und Anwendungen wie die Simulation komplexer elektronischer Schaltungen unmöglich wäre.Für Anwender und interessierte Mathematiker bietet dieses Werk erstmals einen mathematisch fundierten Einblick in diese Thematik.

Wahrscheinlichkeitstheorie und Stochastische Prozesse


Author: Michael Mürmann
Publisher: Springer-Verlag
ISBN: 364238160X
Category: Mathematics
Page: 428
View: 8549

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Dieses Lehrbuch beschäftigt sich mit den zentralen Gebieten einer maßtheoretisch orientierten Wahrscheinlichkeitstheorie im Umfang einer zweisemestrigen Vorlesung. Nach den Grundlagen werden Grenzwertsätze und schwache Konvergenz behandelt. Es folgt die Darstellung und Betrachtung der stochastischen Abhängigkeit durch die bedingte Erwartung, die mit der Radon-Nikodym-Ableitung realisiert wird. Sie wird angewandt auf die Theorie der stochastischen Prozesse, die nach der allgemeinen Konstruktion aus der Untersuchung von Martingalen und Markov-Prozessen besteht. Neu in einem Lehrbuch über allgemeine Wahrscheinlichkeitstheorie ist eine Einführung in die stochastische Analysis von Semimartingalen auf der Grundlage einer geeigneten Stetigkeitsbedingung mit Anwendungen auf die Theorie der Finanzmärkte. Das Buch enthält zahlreiche Übungen, teilweise mit Lösungen. Neben der Theorie vertiefen Anmerkungen, besonders zu mathematischen Modellen für Phänomene der Realität, das Verständnis.​

Elementare Wahrscheinlichkeitstheorie und stochastische Prozesse


Author: Kai L. Chung
Publisher: Springer-Verlag
ISBN: 3642670334
Category: Mathematics
Page: 346
View: 9037

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Aus den Besprechungen: "Unter den zahlreichen Einführungen in die Wahrscheinlichkeitsrechnung bildet dieses Buch eine erfreuliche Ausnahme. Der Stil einer lebendigen Vorlesung ist über Niederschrift und Übersetzung hinweg erhalten geblieben. In jedes Kapitel wird sehr anschaulich eingeführt. Sinn und Nützlichkeit der mathematischen Formulierungen werden den Lesern nahegebracht. Die wichtigsten Zusammenhänge sind als mathematische Sätze klar formuliert." #FREQUENZ#1

Kalman-Bucy-Filter

determinist. Beobachtung u. stochast. Filterung
Author: Karl Brammer,Gerhard Siffling
Publisher: N.A
ISBN: N.A
Category: Control theory
Page: 232
View: 864

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Das Buch will die mannigfaltigen Aufgaben der heutigen Regelungs- und Steuerungstechnik und ihre Lösung nahebringen. Das soll mit möglichst geringem Zeit- und Arbeitsaufwand für den Leser verbunden sein. Leichte Verständlichkeit, Anschaulichkeit und Anwendungsnähe sind deshalb Hauptgesichtspunkt der Darstellung. Vollständigkeit ist nicht angestrebt, vielmehr Darstellung des Wesentlichen. Mathematische Methoden werden auf das Notwendige beschränkt.

Stochastic Processes with Applications


Author: Rabi N. Bhattacharya,Edward C. Waymire
Publisher: SIAM
ISBN: 0898716896
Category: Mathematics
Page: 184
View: 5581

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This book develops systematically and rigorously, yet in an expository and lively manner, the evolution of general random processes and their large time properties such as transience, recurrence, and convergence to steady states. The emphasis is on the most important classes of these processes from the viewpoint of theory as well as applications, namely, Markov processes. The book features very broad coverage of the most applicable aspects of stochastic processes, including sufficient material for self-contained courses on random walks in one and multiple dimensions; Markov chains in discrete and continuous times, including birth-death processes; Brownian motion and diffusions; stochastic optimization; and stochastic differential equations. This book is for graduate students in mathematics, statistics, science and engineering, and it may also be used as a reference by professionals in diverse fields whose work involves the application of probability.

A Basic Course in Measure and Probability

Theory for Applications
Author: Ross Leadbetter,Stamatis Cambanis,Vladas Pipiras
Publisher: Cambridge University Press
ISBN: 1107020409
Category: Mathematics
Page: 376
View: 2916

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A concise introduction covering all of the measure theory and probability most useful for statisticians.

Stochastic Processes with Applications to Finance


Author: Masaaki Kijima
Publisher: CRC Press
ISBN: 9781584882244
Category: Mathematics
Page: 288
View: 2893

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In recent years, modeling financial uncertainty using stochastic processes has become increasingly important, but it is commonly perceived as requiring a deep mathematical background. Stochastic Processes with Applications to Finance shows that this is not necessarily so. It presents the theory of discrete stochastic processes and their applications in finance in an accessible treatment that strikes a balance between the abstract and the practical. Using an approach that views sophisticated stochastic calculus as based on a simple class of discrete processes-"random walks"-the author first provides an elementary introduction to the relevant areas of real analysis and probability. He then uses random walks to explain the change of measure formula, the reflection principle, and the Kolmogorov backward equation. The Black-Scholes formula is derived as a limit of binomial model, and applications to the pricing of derivative securities are presented. Another primary focus of the book is the pricing of corporate bonds and credit derivatives, which the author explains in terms of discrete default models. By presenting important results in discrete processes and showing how to transfer those results to their continuous counterparts, Stochastic Processes with Applications to Finance imparts an intuitive and practical understanding of the subject. This unique treatment is ideal both as a text for a graduate-level class and as a reference for researchers and practitioners in financial engineering, operations research, and mathematical and statistical finance.

Stochastic Processes

Theory and Methods
Author: D. N. Shanbhag,Calyampudi Radhakrishna Rao
Publisher: Gulf Professional Publishing
ISBN: 9780444500144
Category: Mathematics
Page: 967
View: 7735

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J. Neyman, one of the pioneers in laying the foundations of modern statistical theory, stressed the importance of stochastic processes in a paper written in 1960 in the following terms: Currently in the period of dynamic indeterminism in science, there is hardly a serious piece of research, if treated realistically, does not involve operations on stochastic processes. Arising from the need to solve practical problems, several major advances have taken place in the theory of stochastic processes and their applications. Books by Doob (1953; J. Wiley and Sons), Feller (1957, 1966; J. Wiley and Sons) and Loeve (1960; D. van Nostrand and Col., Inc.) among others, have created growing awareness and interest in the use of stochastic processes in scientific and technological studies.The literature on stochastic processes is very extensive and is distributed in several books and journals.

Theory and Applications of Stochastic Processes

An Analytical Approach
Author: Zeev Schuss
Publisher: Springer Science & Business Media
ISBN: 1441916059
Category: Mathematics
Page: 468
View: 9405

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Stochastic processes and diffusion theory are the mathematical underpinnings of many scientific disciplines, including statistical physics, physical chemistry, molecular biophysics, communications theory and many more. Many books, reviews and research articles have been published on this topic, from the purely mathematical to the most practical. This book offers an analytical approach to stochastic processes that are most common in the physical and life sciences, as well as in optimal control and in the theory of filltering of signals from noisy measurements. Its aim is to make probability theory in function space readily accessible to scientists trained in the traditional methods of applied mathematics, such as integral, ordinary, and partial differential equations and asymptotic methods, rather than in probability and measure theory.

Filtering for Stochastic Processes with Applications to Guidance


Author: Richard S. Bucy,Peter D. Joseph
Publisher: American Mathematical Soc.
ISBN: 9780821837825
Category: Mathematics
Page: 217
View: 1400

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This second edition preserves the original text of 1968, with clarification and added references. From the Preface to the Second Edition: ``Since the First Edition of this book, numerous important results have appeared--in particular stochastic integrals with respect to martingales, random fields, Riccati equation theory and realization of nonlinear filters, to name a few. In Appendix D, an attempt is made to provide some of the references that the authors have found useful and to comment on the relation of the cited references to the field ... [W]e hope that this new edition will have the effect of hastening the day when the nonlinear filter will enjoy the same popularity in applications as the linear filter does now.''

Stochastic Processes

Basic Theory and Its Applications
Author: Narahari Umanath Prabhu
Publisher: World Scientific
ISBN: 9812706267
Category: Mathematics
Page: 341
View: 8167

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Most introductory textbooks on stochastic processes which cover standard topics such as Poisson process, Brownian motion, renewal theory and random walks deal inadequately with their applications. Written in a simple and accessible manner, this book addresses that inadequacy and provides guidelines and tools to study the applications. The coverage includes research developments in Markov property, martingales, regenerative phenomena and Tauberian theorems, and covers measure theory at an elementary level.

Lévy Processes

Theory and Applications
Author: Ole E Barndorff-Nielsen,Thomas Mikosch,Sidney I. Resnick
Publisher: Springer Science & Business Media
ISBN: 1461201977
Category: Mathematics
Page: 418
View: 1682

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A Lévy process is a continuous-time analogue of a random walk, and as such, is at the cradle of modern theories of stochastic processes. Martingales, Markov processes, and diffusions are extensions and generalizations of these processes. In the past, representatives of the Lévy class were considered most useful for applications to either Brownian motion or the Poisson process. Nowadays the need for modeling jumps, bursts, extremes and other irregular behavior of phenomena in nature and society has led to a renaissance of the theory of general Lévy processes. Researchers and practitioners in fields as diverse as physics, meteorology, statistics, insurance, and finance have rediscovered the simplicity of Lévy processes and their enormous flexibility in modeling tails, dependence and path behavior. This volume, with an excellent introductory preface, describes the state-of-the-art of this rapidly evolving subject with special emphasis on the non-Brownian world. Leading experts present surveys of recent developments, or focus on some most promising applications. Despite its special character, every topic is aimed at the non- specialist, keen on learning about the new exciting face of a rather aged class of processes. An extensive bibliography at the end of each article makes this an invaluable comprehensive reference text. For the researcher and graduate student, every article contains open problems and points out directions for futurearch. The accessible nature of the work makes this an ideal introductory text for graduate seminars in applied probability, stochastic processes, physics, finance, and telecommunications, and a unique guide to the world of Lévy processes.

An Introduction to Continuous-Time Stochastic Processes

Theory, Models, and Applications to Finance, Biology, and Medicine
Author: Vincenzo Capasso,David Bakstein
Publisher: Springer Science & Business Media
ISBN: 9780817644284
Category: Mathematics
Page: 344
View: 7476

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This concisely written book is a rigorous and self-contained introduction to the theory of continuous-time stochastic processes. Balancing theory and applications, the authors use stochastic methods and concrete examples to model real-world problems from engineering, biomathematics, biotechnology, and finance. Suitable as a textbook for graduate or advanced undergraduate courses, the work may also be used for self-study or as a reference. The book will be of interest to students, pure and applied mathematicians, and researchers or practitioners in mathematical finance, biomathematics, physics, and engineering.

Stochastic Processes with Applications to Finance, Second Edition


Author: Masaaki Kijima
Publisher: CRC Press
ISBN: 143988482X
Category: Business & Economics
Page: 343
View: 9419

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Financial engineering has been proven to be a useful tool for risk management, but using the theory in practice requires a thorough understanding of the risks and ethical standards involved. Stochastic Processes with Applications to Finance, Second Edition presents the mathematical theory of financial engineering using only basic mathematical tools that are easy to understand even for those with little mathematical expertise. This second edition covers several important developments in the financial industry. New to the Second Edition A chapter on the change of measures and pricing of insurance products Many examples of the change of measure technique, including its use in asset pricing theory A section on the use of copulas, especially in the pricing of CDOs Two chapters that offer more coverage of interest rate derivatives and credit derivatives Exploring the merge of actuarial science and financial engineering, this edition examines how the pricing of insurance products, such as equity-linked annuities, requires knowledge of asset pricing theory since the equity index can be traded in the market. The book looks at the development of many probability transforms for pricing insurance risks, including the Esscher transform. It also describes how the copula model is used to model the joint distribution of underlying assets. By presenting significant results in discrete processes and showing how to transfer the results to their continuous counterparts, this text imparts an accessible, practical understanding of the subject. It helps readers not only grasp the theory of financial engineering, but also implement the theory in business.

Stochastik

Einführung in die Wahrscheinlichkeitstheorie und Statistik
Author: Hans-Otto Georgii
Publisher: Walter de Gruyter GmbH & Co KG
ISBN: 3110359707
Category: Mathematics
Page: 448
View: 6537

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Due to the extremely positive reception of this textbook, it is now being published in its 5th edition. The book provides an introduction to the key ideas and elements of probability theory and statistics. Stochastic concepts, models, and methods are highlighted through typical application examples, then analyzed theoretically and systematically explored.

Engineering applications of stochastic processes

theory, problems and solutions
Author: Alexander Zayezdny,Daniel Tabak,Dov Wulich,Peter Smith
Publisher: Research Studie
ISBN: N.A
Category: Science
Page: 509
View: 9653

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A concise, systematic treatment of probabilistic calculations of the sort used in electronic communication, radar, and automatic control. Appropriate as a text in stochastic processes, statistical communication methods, or automatic control. First section discusses random variables. Second section deals with random processes, and response of linear systems to random processes. Each theoretical topic is followed by a description of the associated computational procedures. Chapters contain problems, with solutions.

Stochastic Processes and Filtering Theory


Author: Andrew H. Jazwinski
Publisher: Academic Press
ISBN: 0080960901
Category: Mathematics
Page: 376
View: 4428

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This book presents a unified treatment of linear and nonlinear filtering theory for engineers, with sufficient emphasis on applications to enable the reader to use the theory. The need for this book is twofold. First, although linear estimation theory is relatively well known, it is largely scattered in the journal literature and has not been collected in a single source. Second, available literature on the continuous nonlinear theory is quite esoteric and controversial, and thus inaccessible to engineers uninitiated in measure theory and stochastic differential equations. Furthermore, it is not clear from the available literature whether the nonlinear theory can be applied to practical engineering problems. In attempting to fill the stated needs, the author has retained as much mathematical rigor as he felt was consistent with the prime objective—to explain the theory to engineers. Thus, the author has avoided measure theory in this book by using mean square convergence, on the premise that everyone knows how to average. As a result, the author only requires of the reader background in advanced calculus, theory of ordinary differential equations, and matrix analysis.