Stochastic Processes Basic Theory And Its Applications

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Stochastic Processes

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Author : Narahari Umanath Prabhu
language : en
Publisher: World Scientific
Release Date : 2007

Stochastic Processes written by Narahari Umanath Prabhu and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007 with Mathematics categories.

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.

Stochastic Processes

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Author : Narahari Umanath Prabhu
language : en
Publisher:
Release Date : 2007

Stochastic Processes written by Narahari Umanath Prabhu and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007 with Electronic books categories.

Probability Theory And Stochastic Processes

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Author : Pierre Brémaud
language : en
Publisher: Springer Nature
Release Date : 2020-04-07

Probability Theory And Stochastic Processes written by Pierre Brémaud and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-04-07 with Mathematics categories.

The ultimate objective of this book is to present a panoramic view of the main stochastic processes which have an impact on applications, with complete proofs and exercises. Random processes play a central role in the applied sciences, including operations research, insurance, finance, biology, physics, computer and communications networks, and signal processing. In order to help the reader to reach a level of technical autonomy sufficient to understand the presented models, this book includes a reasonable dose of probability theory. On the other hand, the study of stochastic processes gives an opportunity to apply the main theoretical results of probability theory beyond classroom examples and in a non-trivial manner that makes this discipline look more attractive to the applications-oriented student. One can distinguish three parts of this book. The first four chapters are about probability theory, Chapters 5 to 8 concern random sequences, or discrete-time stochastic processes, and the rest of the book focuses on stochastic processes and point processes. There is sufficient modularity for the instructor or the self-teaching reader to design a course or a study program adapted to her/his specific needs. This book is in a large measure self-contained.

Stochastic Models Analysis And Applications

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Author : B. R. Bhat
language : en
Publisher: New Age International
Release Date : 2004

Stochastic Models Analysis And Applications written by B. R. Bhat and has been published by New Age International this book supported file pdf, txt, epub, kindle and other format this book has been release on 2004 with Mathematical statistics categories.

The Book Presents A Systematic Exposition Of The Basic Theory And Applications Of Stochastic Models.Emphasising The Modelling Rather Than Mathematical Aspects Of Stochastic Processes, The Book Bridges The Gap Between The Theory And Applications Of These Processes.The Basic Building Blocks Of Model Construction Are Explained In A Step By Step Manner, Starting From The Simplest Model Of Random Walk And Proceeding Gradually To More Complicated Models. Several Examples Are Given Throughout The Text To Illustrate Important Analytical Properties As Well As To Provide Applications.The Book Also Includes A Detailed Chapter On Inference For Stochastic Processes. This Chapter Highlights Some Of The Recent Developments In The Subject And Explains Them Through Illustrative Examples.An Important Feature Of The Book Is The Complements And Problems Section At The End Of Each Chapter Which Presents (I) Additional Properties Of The Model, (Ii) Extensions Of The Model, And (Iii) Applications Of The Model To Different Areas.With All These Features, This Is An Invaluable Text For Post-Graduate Students Of Statistics, Mathematics And Operation Research.

Point Process Theory And Applications

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Author : Martin Jacobsen
language : en
Publisher: Springer Science & Business Media
Release Date : 2006-07-27

Point Process Theory And Applications written by Martin Jacobsen 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 2006-07-27 with Mathematics categories.

The book aims at presenting a detailed and mathematically rigorous exposition of the theory and applications of a class of point processes and piecewise deterministic p- cesses. The framework is suf?ciently general to unify the treatment of several classes of stochastic phenomena: point processes, Markov chains and other Markov processes in continuous time, semi-Markov processes, queueing and storage models, and li- lihood processes. There are applications to ?nance, insurance and risk, population models, survival analysis, and congestion models. A major aim has been to show the versatility of piecewise deterministic Markov processes for applications and to show how they may also become useful in areas where thus far they have not been much in evidence. Originally the plan was to develop a graduate text on marked point processes - dexed by time which would focus on probabilistic structure and be essentially se- contained. However, it soon became apparent that the discussion should naturally include a traditional class of continuous time stochastic processes constructed from certain marked point processes. This class consists of ‘piecewise deterministic p- cesses’; that is, processes with ?nitely many jumps on ?nite time intervals which, roughly speaking, develop deterministically between the random jump times. The - position starts with the point process theory and then uses this to treat the piecewise deterministic processes.

An Introduction To Stochastic Processes And Their Applications

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Author : Petar Todorovic
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06

An Introduction To Stochastic Processes And Their Applications written by Petar Todorovic 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 2012-12-06 with Mathematics categories.

This text on stochastic processes and their applications is based on a set of lectures given during the past several years at the University of California, Santa Barbara (UCSB). It is an introductory graduate course designed for classroom purposes. Its objective is to provide graduate students of statistics with an overview of some basic methods and techniques in the theory of stochastic processes. The only prerequisites are some rudiments of measure and integration theory and an intermediate course in probability theory. There are more than 50 examples and applications and 243 problems and complements which appear at the end of each chapter. The book consists of 10 chapters. Basic concepts and definitions are pro vided in Chapter 1. This chapter also contains a number of motivating ex amples and applications illustrating the practical use of the concepts. The last five sections are devoted to topics such as separability, continuity, and measurability of random processes, which are discussed in some detail. The concept of a simple point process on R+ is introduced in Chapter 2. Using the coupling inequality and Le Cam's lemma, it is shown that if its counting function is stochastically continuous and has independent increments, the point process is Poisson. When the counting function is Markovian, the sequence of arrival times is also a Markov process. Some related topics such as independent thinning and marked point processes are also discussed. In the final section, an application of these results to flood modeling is presented.

Mathematics In Science And Engineering

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Author :
language : en
Publisher:
Release Date : 1970

Mathematics In Science And Engineering written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1970 with Engineering mathematics categories.

Mathematical Reviews

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Author :
language : en
Publisher:
Release Date : 2007

Mathematical Reviews written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007 with Mathematics categories.

Introduction To Stochastic Processes

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Author : Mu-fa Chen
language : en
Publisher: World Scientific
Release Date : 2021-05-25

Introduction To Stochastic Processes written by Mu-fa Chen and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-05-25 with Mathematics categories.

The objective of this book is to introduce the elements of stochastic processes in a rather concise manner where we present the two most important parts — Markov chains and stochastic analysis. The readers are led directly to the core of the main topics to be treated in the context. Further details and additional materials are left to a section containing abundant exercises for further reading and studying.In the part on Markov chains, the focus is on the ergodicity. By using the minimal nonnegative solution method, we deal with the recurrence and various types of ergodicity. This is done step by step, from finite state spaces to denumerable state spaces, and from discrete time to continuous time. The methods of proofs adopt modern techniques, such as coupling and duality methods. Some very new results are included, such as the estimate of the spectral gap. The structure and proofs in the first part are rather different from other existing textbooks on Markov chains.In the part on stochastic analysis, we cover the martingale theory and Brownian motions, the stochastic integral and stochastic differential equations with emphasis on one dimension, and the multidimensional stochastic integral and stochastic equation based on semimartingales. We introduce three important topics here: the Feynman-Kac formula, random time transform and Girsanov transform. As an essential application of the probability theory in classical mathematics, we also deal with the famous Brunn-Minkowski inequality in convex geometry.This book also features modern probability theory that is used in different fields, such as MCMC, or even deterministic areas: convex geometry and number theory. It provides a new and direct routine for students going through the classical Markov chains to the modern stochastic analysis.

Stochastic Processes

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Author : Toshio Nakagawa
language : en
Publisher: Springer Science & Business Media
Release Date : 2011-05-27

Stochastic Processes written by Toshio Nakagawa 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 2011-05-27 with Science categories.

Reliability theory is of fundamental importance for engineers and managers involved in the manufacture of high-quality products and the design of reliable systems. In order to make sense of the theory, however, and to apply it to real systems, an understanding of the basic stochastic processes is indispensable. As well as providing readers with useful reliability studies and applications, Stochastic Processes also gives a basic treatment of such stochastic processes as: the Poisson process, the renewal process, the Markov chain, the Markov process, and the Markov renewal process. Many examples are cited from reliability models to show the reader how to apply stochastic processes. Furthermore, Stochastic Processes gives a simple introduction to other stochastic processes such as the cumulative process, the Wiener process, the Brownian motion and reliability applications. Stochastic Processes is suitable for use as a reliability textbook by advanced undergraduate and graduate students. It is also of interest to researchers, engineers and managers who study or practise reliability and maintenance.