Adventures in Stochastic Processes

Filename: adventures-in-stochastic-processes.pdf
ISBN: 9781461203872
Release Date: 2013-12-11
Number of pages: 626
Author: Sidney I. Resnick
Publisher: Springer Science & Business Media

Download and read online Adventures in Stochastic Processes in PDF and EPUB 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.


Adventures in Stochastic Processes

Filename: adventures-in-stochastic-processes.pdf
ISBN: 0817635912
Release Date: 1992-09-03
Number of pages: 626
Author: Sidney I. Resnick
Publisher: Springer Science & Business Media

Download and read online Adventures in Stochastic Processes in PDF and EPUB Stochastic processes are necessary ingredients for building models of a wide variety of phenomena exhibiting time varying randomness. In a lively and imaginative presentation, studded with examples, exercises, and applications, and supported by inclusion of computational procedures, the author has created a textbook that provides easy access to this fundamental topic for many students of applied sciences at many levels. With its carefully modularized discussion and crystal clear differentiation between rigorous proof and plausibility argument, it is accessible to beginners but flexible enough to serve as well those who come to the course with strong backgrounds. The prerequisite background for reading the book is a graduate level pre-measure theoretic probability course. No knowledge of measure theory is presumed and advanced notions of conditioning are scrupulously avoided until the later chapters of the book. The book can be used for either a one or two semester course as given in departments of mathematics, statistics, operation research, business and management, or a number of engineering departments. Its approach to exercises and applications is practical and serious. Some underlying principles of complex problems and computations are cleanly and quickly delineated through rich vignettes of whimsically imagined Happy Harry and his Optima Street gang’s adventures in a world whose randomness is a never-ending source of both wonder and scientific insight. The tools of applied probability---discrete spaces, Markov chains, renewal theory, point processes, branching processes, random walks, Brownian motion---are presented to the reader in illuminating discussion. Applications include such topics as queuing, storage, risk analysis, genetics, inventory, choice, economics, sociology, and other. Because of the conviction that analysts who build models should know how to build them for each class of process studied, the author has included such constructions.


Adventures in Stochastic Processes

Filename: adventures-in-stochastic-processes.pdf
ISBN: 1461203880
Release Date: 2014-09-12
Number of pages: 640
Author: Sidney I. Resnick
Publisher:

Download and read online Adventures in Stochastic Processes in PDF and EPUB


A Probability Path

Filename: a-probability-path.pdf
ISBN: 081764055X
Release Date: 2003-10-16
Number of pages: 453
Author: Sidney Resnick
Publisher: Springer Science & Business Media

Download and read online A Probability Path in PDF and EPUB Many probability books are written by mathematicians and have the built in bias that the reader is assumed to be a mathematician coming to the material for its beauty. This textbook is geared towards beginning graduate students from a variety of disciplines whose primary focus is not necessarily mathematics for its own sake. Instead, A Probability Path is designed for those requiring a deep understanding of advanced probability for their research in statistics, applied probability, biology, operations research, mathematical finance, and engineering.


Basics of Applied Stochastic Processes

Filename: basics-of-applied-stochastic-processes.pdf
ISBN: 9783540893325
Release Date: 2009-01-24
Number of pages: 443
Author: Richard Serfozo
Publisher: Springer Science & Business Media

Download and read online Basics of Applied Stochastic Processes in PDF and EPUB 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.


Introduction to Stochastic Processes Second Edition

Filename: introduction-to-stochastic-processes-second-edition.pdf
ISBN: 158488651X
Release Date: 2006-05-16
Number of pages: 248
Author: Gregory F. Lawler
Publisher: CRC Press

Download and read online Introduction to Stochastic Processes Second Edition in PDF and EPUB Emphasizing fundamental mathematical ideas rather than proofs, Introduction to Stochastic Processes, Second Edition provides quick access to important foundations of probability theory applicable to problems in many fields. Assuming that you have a reasonable level of computer literacy, the ability to write simple programs, and the access to software for linear algebra computations, the author approaches the problems and theorems with a focus on stochastic processes evolving with time, rather than a particular emphasis on measure theory. For those lacking in exposure to linear differential and difference equations, the author begins with a brief introduction to these concepts. He proceeds to discuss Markov chains, optimal stopping, martingales, and Brownian motion. The book concludes with a chapter on stochastic integration. The author supplies many basic, general examples and provides exercises at the end of each chapter. New to the Second Edition: Expanded chapter on stochastic integration that introduces modern mathematical finance Introduction of Girsanov transformation and the Feynman-Kac formula Expanded discussion of Itô's formula and the Black-Scholes formula for pricing options New topics such as Doob's maximal inequality and a discussion on self similarity in the chapter on Brownian motion Applicable to the fields of mathematics, statistics, and engineering as well as computer science, economics, business, biological science, psychology, and engineering, this concise introduction is an excellent resource both for students and professionals.


Stochastic Processes

Filename: stochastic-processes.pdf
ISBN: 9781107435315
Release Date: 2013-12-12
Number of pages: 568
Author: Robert G. Gallager
Publisher: Cambridge University Press

Download and read online Stochastic Processes in PDF and EPUB 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.


Essentials of Stochastic Processes

Filename: essentials-of-stochastic-processes.pdf
ISBN: 9783319456140
Release Date: 2016-11-07
Number of pages: 275
Author: Richard Durrett
Publisher: Springer

Download and read online Essentials of Stochastic Processes in PDF and EPUB 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.


Heavy Tail Phenomena

Filename: heavy-tail-phenomena.pdf
ISBN: 9780387242729
Release Date: 2007
Number of pages: 404
Author: Sidney I. Resnick
Publisher: Springer Science & Business Media

Download and read online Heavy Tail Phenomena in PDF and EPUB This comprehensive text gives an interesting and useful blend of the mathematical, probabilistic and statistical tools used in heavy-tail analysis. Heavy tails are characteristic of many phenomena where the probability of a single huge value impacts heavily. Record-breaking insurance losses, financial-log returns, files sizes stored on a server, transmission rates of files are all examples of heavy-tailed phenomena. Key features: * Unique text devoted to heavy-tails * Emphasizes both probability modeling and statistical methods for fitting models. Most treatments focus on one or the other but not both * Presents broad applicability of heavy-tails to the fields of data networks, finance (e.g., value-at- risk), insurance, and hydrology * Clear, efficient and coherent exposition, balancing theory and actual data to show the applicability and limitations of certain methods * Examines in detail the mathematical properties of the methodologies as well as their implementation in Splus or R statistical languages * Exposition driven by numerous examples and exercises Prerequisites for the reader include a prior course in stochastic processes and probability, some statistical background, some familiarity with time series analysis, and ability to use (or at least to learn) a statistics package such as R or Splus. This work will serve second-year graduate students and researchers in the areas of applied mathematics, statistics, operations research, electrical engineering, and economics.


A Natural Introduction to Probability Theory

Filename: a-natural-introduction-to-probability-theory.pdf
ISBN: 3764321881
Release Date: 2003
Number of pages: 191
Author: Ronald Meester
Publisher: Springer Science & Business Media

Download and read online A Natural Introduction to Probability Theory in PDF and EPUB "The book provides an introduction, in full rigour, of discrete and continuous probability, without using algebras or sigma-algebras; only familiarity with first-year calculus is required. Starting with the framework of discrete probability, it is already possible to discuss random walk, weak laws of large numbers and a first central limit theorem. After that, continuous probability, infinitely many repetitions, strong laws of large numbers, and branching processes are extensively treated. Finally, weak convergence is introduced and the central limit theorem is proved." "The theory is illustrated with many original and surprising examples and problems, taken from classical applications like gambling, geometry or graph theory, as well as from applications in biology, medicine, social sciences, sports, and coding theory."--BOOK JACKET.


Brownian Motion

Filename: brownian-motion.pdf
ISBN: 9783110307306
Release Date: 2014-06-18
Number of pages: 424
Author: René L. Schilling
Publisher: Walter de Gruyter GmbH & Co KG

Download and read online Brownian Motion in PDF and EPUB Stochastic processes occur everywhere in sciences and engineering, and need to be understood by applied mathematicians, engineers and scientists alike. This is a first course introducing the reader gently to the subject. Brownian motions are a stochastic process, central to many applications and easy to treat.


Percolation

Filename: percolation.pdf
ISBN: 9783662039816
Release Date: 2013-03-09
Number of pages: 447
Author: Geoffrey R. Grimmett
Publisher: Springer Science & Business Media

Download and read online Percolation in PDF and EPUB Percolation theory is the study of an idealized random medium in two or more dimensions. The emphasis of this book is upon core mathematical material and the presentation of the shortest and most accessible proofs. Much new material appears in this second edition including dynamic and static renormalization, strict inequalities between critical points, a sketch of the lace expansion, and several essays on related fields and applications.


Stochastic Models Information Theory and Lie Groups Volume 1

Filename: stochastic-models-information-theory-and-lie-groups-volume-1.pdf
ISBN: 9780817648039
Release Date: 2009-09-02
Number of pages: 383
Author: Gregory S. Chirikjian
Publisher: Springer Science & Business Media

Download and read online Stochastic Models Information Theory and Lie Groups Volume 1 in PDF and EPUB This unique two-volume set presents the subjects of stochastic processes, information theory, and Lie groups in a unified setting, thereby building bridges between fields that are rarely studied by the same people. Unlike the many excellent formal treatments available for each of these subjects individually, the emphasis in both of these volumes is on the use of stochastic, geometric, and group-theoretic concepts in the modeling of physical phenomena. Stochastic Models, Information Theory, and Lie Groups will be of interest to advanced undergraduate and graduate students, researchers, and practitioners working in applied mathematics, the physical sciences, and engineering. Extensive exercises and motivating examples make the work suitable as a textbook for use in courses that emphasize applied stochastic processes or differential geometry.


Stochastic Simulation Algorithms and Analysis

Filename: stochastic-simulation-algorithms-and-analysis.pdf
ISBN: 9780387690339
Release Date: 2007-07-14
Number of pages: 476
Author: Søren Asmussen
Publisher: Springer Science & Business Media

Download and read online Stochastic Simulation Algorithms and Analysis in PDF and EPUB Sampling-based computational methods have become a fundamental part of the numerical toolset of practitioners and researchers across an enormous number of different applied domains and academic disciplines. This book provides a broad treatment of such sampling-based methods, as well as accompanying mathematical analysis of the convergence properties of the methods discussed. The reach of the ideas is illustrated by discussing a wide range of applications and the models that have found wide usage. The first half of the book focuses on general methods; the second half discusses model-specific algorithms. Exercises and illustrations are included.


Introduction to Stochastic Processes Second Edition

Filename: introduction-to-stochastic-processes-second-edition.pdf
ISBN: 158488651X
Release Date: 2006-05-16
Number of pages: 248
Author: Gregory F. Lawler
Publisher: CRC Press

Download and read online Introduction to Stochastic Processes Second Edition in PDF and EPUB Emphasizing fundamental mathematical ideas rather than proofs, Introduction to Stochastic Processes, Second Edition provides quick access to important foundations of probability theory applicable to problems in many fields. Assuming that you have a reasonable level of computer literacy, the ability to write simple programs, and the access to software for linear algebra computations, the author approaches the problems and theorems with a focus on stochastic processes evolving with time, rather than a particular emphasis on measure theory. For those lacking in exposure to linear differential and difference equations, the author begins with a brief introduction to these concepts. He proceeds to discuss Markov chains, optimal stopping, martingales, and Brownian motion. The book concludes with a chapter on stochastic integration. The author supplies many basic, general examples and provides exercises at the end of each chapter. New to the Second Edition: Expanded chapter on stochastic integration that introduces modern mathematical finance Introduction of Girsanov transformation and the Feynman-Kac formula Expanded discussion of Itô's formula and the Black-Scholes formula for pricing options New topics such as Doob's maximal inequality and a discussion on self similarity in the chapter on Brownian motion Applicable to the fields of mathematics, statistics, and engineering as well as computer science, economics, business, biological science, psychology, and engineering, this concise introduction is an excellent resource both for students and professionals.