Discrete Stochastic Processes And Applications

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Discrete Stochastic Processes

Author : Robert G. Gallager
Publisher : Springer Science & Business Media
ISBN 13 : 146152329X
Total Pages : 280 pages
Book Rating : 4.4/5 (615 download)

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Book Synopsis Discrete Stochastic Processes by : Robert G. Gallager

Download or read book Discrete Stochastic Processes written by Robert G. Gallager and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 280 pages. Available in PDF, EPUB and Kindle. Book excerpt: Stochastic processes are found in probabilistic systems that evolve with time. Discrete stochastic processes change by only integer time steps (for some time scale), or are characterized by discrete occurrences at arbitrary times. Discrete Stochastic Processes helps the reader develop the understanding and intuition necessary to apply stochastic process theory in engineering, science and operations research. The book approaches the subject via many simple examples which build insight into the structure of stochastic processes and the general effect of these phenomena in real systems. The book presents mathematical ideas without recourse to measure theory, using only minimal mathematical analysis. In the proofs and explanations, clarity is favored over formal rigor, and simplicity over generality. Numerous examples are given to show how results fail to hold when all the conditions are not satisfied. Audience: An excellent textbook for a graduate level course in engineering and operations research. Also an invaluable reference for all those requiring a deeper understanding of the subject.

Stochastic Processes

Author : Robert G. Gallager
Publisher : Cambridge University Press
ISBN 13 : 1107039754
Total Pages : 559 pages
Book Rating : 4.1/5 (7 download)

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Book Synopsis Stochastic Processes by : Robert G. Gallager

Download or read book Stochastic Processes written by Robert G. Gallager and published by Cambridge University Press. This book was released on 2013-12-12 with total page 559 pages. Available in PDF, EPUB and Kindle. Book excerpt: The definitive textbook on stochastic processes, written by one of the world's leading information theorists, covering both theory and applications.

Discrete Stochastic Processes and Applications

Author : Jean-François Collet
Publisher : Springer
ISBN 13 : 3319740180
Total Pages : 228 pages
Book Rating : 4.3/5 (197 download)

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Book Synopsis Discrete Stochastic Processes and Applications by : Jean-François Collet

Download or read book Discrete Stochastic Processes and Applications written by Jean-François Collet and published by Springer. This book was released on 2018-04-05 with total page 228 pages. Available in PDF, EPUB and Kindle. Book excerpt: This unique text for beginning graduate students gives a self-contained introduction to the mathematical properties of stochastics and presents their applications to Markov processes, coding theory, population dynamics, and search engine design. The book is ideal for a newly designed course in an introduction to probability and information theory. Prerequisites include working knowledge of linear algebra, calculus, and probability theory. The first part of the text focuses on the rigorous theory of Markov processes on countable spaces (Markov chains) and provides the basis to developing solid probabilistic intuition without the need for a course in measure theory. The approach taken is gradual beginning with the case of discrete time and moving on to that of continuous time. The second part of this text is more applied; its core introduces various uses of convexity in probability and presents a nice treatment of entropy.

Stochastic Processes with Applications to Finance

Author : Masaaki Kijima
Publisher : CRC Press
ISBN 13 : 1439884846
Total Pages : 345 pages
Book Rating : 4.4/5 (398 download)

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Book Synopsis Stochastic Processes with Applications to Finance by : Masaaki Kijima

Download or read book Stochastic Processes with Applications to Finance written by Masaaki Kijima and published by CRC Press. This book was released on 2016-04-19 with total page 345 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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

Stochastic Processes

Author : Pierre Del Moral
Publisher : CRC Press
ISBN 13 : 1498701841
Total Pages : 866 pages
Book Rating : 4.4/5 (987 download)

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Book Synopsis Stochastic Processes by : Pierre Del Moral

Download or read book Stochastic Processes written by Pierre Del Moral and published by CRC Press. This book was released on 2017-02-24 with total page 866 pages. Available in PDF, EPUB and Kindle. Book excerpt: Unlike traditional books presenting stochastic processes in an academic way, this book includes concrete applications that students will find interesting such as gambling, finance, physics, signal processing, statistics, fractals, and biology. Written with an important illustrated guide in the beginning, it contains many illustrations, photos and pictures, along with several website links. Computational tools such as simulation and Monte Carlo methods are included as well as complete toolboxes for both traditional and new computational techniques.

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.

An Introduction to Stochastic Processes and Their Applications

Author : Petar Todorovic
Publisher : Springer Science & Business Media
ISBN 13 : 1461397421
Total Pages : 302 pages
Book Rating : 4.4/5 (613 download)

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Book Synopsis An Introduction to Stochastic Processes and Their Applications by : Petar Todorovic

Download or read book An Introduction to Stochastic Processes and Their Applications written by Petar Todorovic and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 302 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Stochastic Processes with Applications

Author : Rabi N. Bhattacharya
Publisher : SIAM
ISBN 13 : 0898716896
Total Pages : 726 pages
Book Rating : 4.8/5 (987 download)

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Book Synopsis Stochastic Processes with Applications by : Rabi N. Bhattacharya

Download or read book Stochastic Processes with Applications written by Rabi N. Bhattacharya and published by SIAM. This book was released on 2009-08-27 with total page 726 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Probability Theory and Stochastic Processes with Applications (Second Edition)

Author : Oliver Knill
Publisher : World Scientific Publishing Company
ISBN 13 : 9789813109490
Total Pages : 500 pages
Book Rating : 4.1/5 (94 download)

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Book Synopsis Probability Theory and Stochastic Processes with Applications (Second Edition) by : Oliver Knill

Download or read book Probability Theory and Stochastic Processes with Applications (Second Edition) written by Oliver Knill and published by World Scientific Publishing Company. This book was released on 2017-01-31 with total page 500 pages. Available in PDF, EPUB and Kindle. Book excerpt: This second edition has a unique approach that provides a broad and wide introduction into the fascinating area of probability theory. It starts on a fast track with the treatment of probability theory and stochastic processes by providing short proofs. The last chapter is unique as it features a wide range of applications in other fields like Vlasov dynamics of fluids, statistics of circular data, singular continuous random variables, Diophantine equations, percolation theory, random Schrödinger operators, spectral graph theory, integral geometry, computer vision, and processes with high risk.Many of these areas are under active investigation and this volume is highly suited for ambitious undergraduate students, graduate students and researchers.

The Elements of Stochastic Processes with Applications to the Natural Sciences

Author : Norman T. J. Bailey
Publisher : John Wiley & Sons
ISBN 13 : 9780471523680
Total Pages : 268 pages
Book Rating : 4.5/5 (236 download)

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Book Synopsis The Elements of Stochastic Processes with Applications to the Natural Sciences by : Norman T. J. Bailey

Download or read book The Elements of Stochastic Processes with Applications to the Natural Sciences written by Norman T. J. Bailey and published by John Wiley & Sons. This book was released on 1991-01-16 with total page 268 pages. Available in PDF, EPUB and Kindle. Book excerpt: Develops an introductory and relatively simple account of the theory and application of the evolutionary type of stochastic process. Professor Bailey adopts the heuristic approach of applied mathematics and develops both theoretical principles and applied techniques simultaneously.

Basics of Applied Stochastic Processes

Author : Richard Serfozo
Publisher : Springer Science & Business Media
ISBN 13 : 3540893326
Total Pages : 452 pages
Book Rating : 4.5/5 (48 download)

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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.

Stochastic Analysis in Discrete and Continuous Settings

Author : Nicolas Privault
Publisher : Springer
ISBN 13 : 3642023800
Total Pages : 322 pages
Book Rating : 4.6/5 (42 download)

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Book Synopsis Stochastic Analysis in Discrete and Continuous Settings by : Nicolas Privault

Download or read book Stochastic Analysis in Discrete and Continuous Settings written by Nicolas Privault and published by Springer. This book was released on 2009-07-14 with total page 322 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph is an introduction to some aspects of stochastic analysis in the framework of normal martingales, in both discrete and continuous time. The text is mostly self-contained, except for Section 5.7 that requires some background in geometry, and should be accessible to graduate students and researchers having already received a basic training in probability. Prereq- sites are mostly limited to a knowledge of measure theory and probability, namely?-algebras,expectations,andconditionalexpectations.Ashortint- duction to stochastic calculus for continuous and jump processes is given in Chapter 2 using normal martingales, whose predictable quadratic variation is the Lebesgue measure. There already exists several books devoted to stochastic analysis for c- tinuous di?usion processes on Gaussian and Wiener spaces, cf. e.g. [51], [63], [65], [72], [83], [84], [92], [128], [134], [143], [146], [147]. The particular f- ture of this text is to simultaneously consider continuous processes and jump processes in the uni?ed framework of normal martingales.

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.

Adventures in Stochastic Processes

Author : Sidney I. Resnick
Publisher : Springer Science & Business Media
ISBN 13 : 1461203872
Total Pages : 640 pages
Book Rating : 4.4/5 (612 download)

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Book Synopsis Adventures in Stochastic Processes by : Sidney I. Resnick

Download or read book Adventures in Stochastic Processes written by Sidney I. Resnick and published by Springer Science & Business Media. This book was released on 2013-12-11 with total page 640 pages. Available in PDF, EPUB and Kindle. Book excerpt: Stochastic processes are necessary ingredients for building models of a wide variety of phenomena exhibiting time varying randomness. This text offers easy access to this fundamental topic for many students of applied sciences at many levels. It includes examples, exercises, applications, and computational procedures. It is uniquely useful for beginners and non-beginners in the field. No knowledge of measure theory is presumed.

A First Look At Stochastic Processes

Author : Jeffrey S Rosenthal
Publisher : World Scientific
ISBN 13 : 9811207925
Total Pages : 213 pages
Book Rating : 4.8/5 (112 download)

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Book Synopsis A First Look At Stochastic Processes by : Jeffrey S Rosenthal

Download or read book A First Look At Stochastic Processes written by Jeffrey S Rosenthal and published by World Scientific. This book was released on 2019-09-26 with total page 213 pages. Available in PDF, EPUB and Kindle. Book excerpt: This textbook introduces the theory of stochastic processes, that is, randomness which proceeds in time. Using concrete examples like repeated gambling and jumping frogs, it presents fundamental mathematical results through simple, clear, logical theorems and examples. It covers in detail such essential material as Markov chain recurrence criteria, the Markov chain convergence theorem, and optional stopping theorems for martingales. The final chapter provides a brief introduction to Brownian motion, Markov processes in continuous time and space, Poisson processes, and renewal theory.Interspersed throughout are applications to such topics as gambler's ruin probabilities, random walks on graphs, sequence waiting times, branching processes, stock option pricing, and Markov Chain Monte Carlo (MCMC) algorithms.The focus is always on making the theory as well-motivated and accessible as possible, to allow students and readers to learn this fascinating subject as easily and painlessly as possible.

Stochastic Processes with Applications to Finance

Author : Masaaki Kijima
Publisher : CRC Press
ISBN 13 : 9781584882244
Total Pages : 290 pages
Book Rating : 4.8/5 (822 download)

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Book Synopsis Stochastic Processes with Applications to Finance by : Masaaki Kijima

Download or read book Stochastic Processes with Applications to Finance written by Masaaki Kijima and published by CRC Press. This book was released on 2002-07-29 with total page 290 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Discrete Time Series, Processes, and Applications in Finance

Author : Gilles Zumbach
Publisher : Springer Science & Business Media
ISBN 13 : 3642317421
Total Pages : 326 pages
Book Rating : 4.6/5 (423 download)

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Book Synopsis Discrete Time Series, Processes, and Applications in Finance by : Gilles Zumbach

Download or read book Discrete Time Series, Processes, and Applications in Finance written by Gilles Zumbach and published by Springer Science & Business Media. This book was released on 2012-10-04 with total page 326 pages. Available in PDF, EPUB and Kindle. Book excerpt: Most financial and investment decisions are based on considerations of possible future changes and require forecasts on the evolution of the financial world. Time series and processes are the natural tools for describing the dynamic behavior of financial data, leading to the required forecasts. This book presents a survey of the empirical properties of financial time series, their descriptions by means of mathematical processes, and some implications for important financial applications used in many areas like risk evaluation, option pricing or portfolio construction. The statistical tools used to extract information from raw data are introduced. Extensive multiscale empirical statistics provide a solid benchmark of stylized facts (heteroskedasticity, long memory, fat-tails, leverage...), in order to assess various mathematical structures that can capture the observed regularities. The author introduces a broad range of processes and evaluates them systematically against the benchmark, summarizing the successes and limitations of these models from an empirical point of view. The outcome is that only multiscale ARCH processes with long memory, discrete multiplicative structures and non-normal innovations are able to capture correctly the empirical properties. In particular, only a discrete time series framework allows to capture all the stylized facts in a process, whereas the stochastic calculus used in the continuum limit is too constraining. The present volume offers various applications and extensions for this class of processes including high-frequency volatility estimators, market risk evaluation, covariance estimation and multivariate extensions of the processes. The book discusses many practical implications and is addressed to practitioners and quants in the financial industry, as well as to academics, including graduate (Master or PhD level) students. The prerequisites are basic statistics and some elementary financial mathematics.