An Introduction To Stochastic Processes And Their Applications

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An Introduction to Stochastic Processes and Their Applications

Petar Todorovic
An Introduction to Stochastic Processes and Their Applications Book PDF

Author : Petar Todorovic
Publisher : Springer Science & Business Media
Page : 302 pages
File Size : 52,5 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781461397427

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An Introduction to Stochastic Processes and Their Applications by Petar Todorovic Pdf

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.

An Introduction to Stochastic Processes and Their Applications

Chin Long Chiang
An Introduction to Stochastic Processes and Their Applications Book PDF

Author : Chin Long Chiang
Publisher : Krieger Publishing Company
Page : 552 pages
File Size : 45,8 Mb
Release : 1980
Category : Biomathematics
ISBN : UOM:39015007663761

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An Introduction to Stochastic Processes and Their Applications by Chin Long Chiang Pdf

Random variables. Probability generating functions. Exponential-type distributions and maximum likelihood estimation. Branching process, random walk and ruin problem. Markov chains. Algebraic treatment of finite Markov chains. Renewal processes. Some stochastic models of population growth. A general birth process, an equality and an epidemic model. Birth-death processes and queueing processes. A simple illness-death process - fix-neyman processes. Multiple transition probabilities in the simple illness death process. Multiple transition time in the simple illness death process - an alternating renewal process. The kolmogorov differential equations and finite markov processes. Kolmogorov differential equations and finite markov processes - continuation. A general illness-death process. Migration processes and birth-illness-death processes.

Stochastic Processes and Applications

Grigorios A. Pavliotis
Stochastic Processes and Applications Book PDF

Author : Grigorios A. Pavliotis
Publisher : Springer
Page : 339 pages
File Size : 52,9 Mb
Release : 2014-11-19
Category : Mathematics
ISBN : 9781493913237

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Stochastic Processes and Applications by Grigorios A. Pavliotis Pdf

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.

Basics of Applied Stochastic Processes

Richard Serfozo
Basics of Applied Stochastic Processes Book PDF

Author : Richard Serfozo
Publisher : Springer Science & Business Media
Page : 452 pages
File Size : 44,6 Mb
Release : 2009-01-24
Category : Mathematics
ISBN : 9783540893325

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Basics of Applied Stochastic Processes by Richard Serfozo Pdf

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

Mu-fa Chen,Yong-hua Mao
Introduction To Stochastic Processes Book PDF

Author : Mu-fa Chen,Yong-hua Mao
Publisher : World Scientific
Page : 245 pages
File Size : 46,6 Mb
Release : 2021-05-25
Category : Mathematics
ISBN : 9789814740326

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Introduction To Stochastic Processes by Mu-fa Chen,Yong-hua Mao Pdf

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.

Introduction to Stochastic Processes with R

Robert P. Dobrow
Introduction to Stochastic Processes with R Book PDF

Author : Robert P. Dobrow
Publisher : John Wiley & Sons
Page : 503 pages
File Size : 42,6 Mb
Release : 2016-03-07
Category : Mathematics
ISBN : 9781118740651

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Introduction to Stochastic Processes with R by Robert P. Dobrow Pdf

An introduction to stochastic processes through the use of R Introduction to Stochastic Processes with R is an accessible and well-balanced presentation of the theory of stochastic processes, with an emphasis on real-world applications of probability theory in the natural and social sciences. The use of simulation, by means of the popular statistical software R, makes theoretical results come alive with practical, hands-on demonstrations. Written by a highly-qualified expert in the field, the author presents numerous examples from a wide array of disciplines, which are used to illustrate concepts and highlight computational and theoretical results. Developing readers’ problem-solving skills and mathematical maturity, Introduction to Stochastic Processes with R features: More than 200 examples and 600 end-of-chapter exercises A tutorial for getting started with R, and appendices that contain review material in probability and matrix algebra Discussions of many timely and stimulating topics including Markov chain Monte Carlo, random walk on graphs, card shuffling, Black–Scholes options pricing, applications in biology and genetics, cryptography, martingales, and stochastic calculus Introductions to mathematics as needed in order to suit readers at many mathematical levels A companion web site that includes relevant data files as well as all R code and scripts used throughout the book Introduction to Stochastic Processes with R is an ideal textbook for an introductory course in stochastic processes. The book is aimed at undergraduate and beginning graduate-level students in the science, technology, engineering, and mathematics disciplines. The book is also an excellent reference for applied mathematicians and statisticians who are interested in a review of the topic.

Stochastic Processes

Robert G. Gallager
Stochastic Processes Book PDF

Author : Robert G. Gallager
Publisher : Cambridge University Press
Page : 559 pages
File Size : 41,6 Mb
Release : 2013-12-12
Category : Business & Economics
ISBN : 9781107039759

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Stochastic Processes by Robert G. Gallager Pdf

The definitive textbook on stochastic processes, written by one of the world's leading information theorists, covering both theory and applications.

Introduction to Stochastic Calculus with Applications

Fima C. Klebaner
Introduction to Stochastic Calculus with Applications Book PDF

Author : Fima C. Klebaner
Publisher : Imperial College Press
Page : 431 pages
File Size : 40,8 Mb
Release : 2005
Category : Mathematics
ISBN : 9781860945557

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Introduction to Stochastic Calculus with Applications by Fima C. Klebaner Pdf

This book presents a concise treatment of stochastic calculus and its applications. It gives a simple but rigorous treatment of the subject including a range of advanced topics, it is useful for practitioners who use advanced theoretical results. It covers advanced applications, such as models in mathematical finance, biology and engineering.Self-contained and unified in presentation, the book contains many solved examples and exercises. It may be used as a textbook by advanced undergraduates and graduate students in stochastic calculus and financial mathematics. It is also suitable for practitioners who wish to gain an understanding or working knowledge of the subject. For mathematicians, this book could be a first text on stochastic calculus; it is good companion to more advanced texts by a way of examples and exercises. For people from other fields, it provides a way to gain a working knowledge of stochastic calculus. It shows all readers the applications of stochastic calculus methods and takes readers to the technical level required in research and sophisticated modelling.This second edition contains a new chapter on bonds, interest rates and their options. New materials include more worked out examples in all chapters, best estimators, more results on change of time, change of measure, random measures, new results on exotic options, FX options, stochastic and implied volatility, models of the age-dependent branching process and the stochastic Lotka-Volterra model in biology, non-linear filtering in engineering and five new figures.Instructors can obtain slides of the text from the author.

Stochastic Processes

Pierre Del Moral,Spiridon Penev
Stochastic Processes Book PDF

Author : Pierre Del Moral,Spiridon Penev
Publisher : CRC Press
Page : 866 pages
File Size : 46,6 Mb
Release : 2017-02-24
Category : Mathematics
ISBN : 9781498701846

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Stochastic Processes by Pierre Del Moral,Spiridon Penev Pdf

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.

An Introduction to Continuous-Time Stochastic Processes

Vincenzo Capasso,David Bakstein
An Introduction to Continuous Time Stochastic Processes Book PDF

Author : Vincenzo Capasso,David Bakstein
Publisher : Springer Science & Business Media
Page : 434 pages
File Size : 46,9 Mb
Release : 2012-07-27
Category : Mathematics
ISBN : 9780817683467

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An Introduction to Continuous-Time Stochastic Processes by Vincenzo Capasso,David Bakstein Pdf

Expanding on the first edition of An Introduction to Continuous-Time Stochastic Processes, this concisely written book is a rigorous and self-contained introduction to the theory of continuous-time stochastic processes. A balance of theory and applications, the work features concrete examples of modeling real-world problems from biology, medicine, industrial applications, finance, and insurance using stochastic methods. No previous knowledge of stochastic processes is required.

Stochastic-Process Limits

Ward Whitt
Stochastic Process Limits Book PDF

Author : Ward Whitt
Publisher : Springer Science & Business Media
Page : 616 pages
File Size : 49,5 Mb
Release : 2006-04-11
Category : Mathematics
ISBN : 9780387217482

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Stochastic-Process Limits by Ward Whitt Pdf

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

Stochastic Processes and Their Applications

Frank Beichelt,L. Paul Fatti
Stochastic Processes and Their Applications Book PDF

Author : Frank Beichelt,L. Paul Fatti
Publisher : CRC Press
Page : 342 pages
File Size : 47,5 Mb
Release : 2001-10-18
Category : Mathematics
ISBN : 0415272327

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Stochastic Processes and Their Applications by Frank Beichelt,L. Paul Fatti Pdf

This book introduces stochastic processes and their applications for students in engineering, industrial statistics, science, operations research, business, and finance. It provides the theoretical foundations for modeling time-dependent random phenomena encountered in these disciplines. Through numerous science and engineering-based examples and exercises, the author presents the subject in a comprehensible, practically oriented way, but he also includes some important proofs and theoretically challenging examples and exercises that will appeal to more mathematically minded readers. Solutions to most of the exercises are included either in an appendix or within the text.

An Introduction to Stochastic Modeling

Howard M. Taylor,Samuel Karlin
An Introduction to Stochastic Modeling Book PDF

Author : Howard M. Taylor,Samuel Karlin
Publisher : Academic Press
Page : 410 pages
File Size : 52,6 Mb
Release : 2014-05-10
Category : Mathematics
ISBN : 9781483269276

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An Introduction to Stochastic Modeling by Howard M. Taylor,Samuel Karlin Pdf

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.

Stochastic Processes in Science, Engineering and Finance

Frank Beichelt
Stochastic Processes in Science Engineering and Finance Book PDF

Author : Frank Beichelt
Publisher : CRC Press
Page : 438 pages
File Size : 45,5 Mb
Release : 2006-02-22
Category : Mathematics
ISBN : 142001045X

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Stochastic Processes in Science, Engineering and Finance by Frank Beichelt Pdf

This book presents a self-contained introduction to stochastic processes with emphasis on their applications in science, engineering, finance, computer science, and operations research. It provides theoretical foundations for modeling time-dependent random phenomena in these areas and illustrates their application by analyzing numerous practical examples. The treatment assumes few prerequisites, requiring only the standard mathematical maturity acquired by undergraduate applied science students. It includes an introductory chapter that summarizes the basic probability theory needed as background. Numerous exercises reinforce the concepts and techniques discussed and allow readers to assess their grasp of the subject. Solutions to most of the exercises are provided in an appendix. While focused primarily on practical aspects, the presentation includes some important proofs along with more challenging examples and exercises for those more theoretically inclined. Mastering the contents of this book prepares readers to apply stochastic modeling in their own fields and enables them to work more creatively with software designed for dealing with the data analysis aspects of stochastic processes.

An Introduction to Stochastic Modeling

Mark Pinsky,Samuel Karlin
An Introduction to Stochastic Modeling Book PDF

Author : Mark Pinsky,Samuel Karlin
Publisher : Academic Press
Page : 585 pages
File Size : 41,9 Mb
Release : 2011
Category : Mathematics
ISBN : 9780123814166

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An Introduction to Stochastic Modeling by Mark Pinsky,Samuel Karlin Pdf

Serving as the foundation for a one-semester course in stochastic processes for students familiar with elementary probability theory and calculus, Introduction to Stochastic Modeling, Fourth Edition, bridges the gap between basic probability and an intermediate level course in stochastic processes. The objectives of the text are to introduce students to the standard concepts and methods of stochastic modeling, to illustrate the rich diversity of applications of stochastic processes in the applied sciences, and to provide exercises in the application of simple stochastic analysis to realistic problems. New to this edition: Realistic applications from a variety of disciplines integrated throughout the text, including more biological applications Plentiful, completely updated problems Completely updated and reorganized end-of-chapter exercise sets, 250 exercises with answers New chapters of stochastic differential equations and Brownian motion and related processes Additional sections on Martingale and Poisson process Realistic applications from a variety of disciplines integrated throughout the text Extensive end of chapter exercises sets, 250 with answers Chapter 1-9 of the new edition are identical to the previous edition New! Chapter 10 - Random Evolutions New! Chapter 11- Characteristic functions and Their Applications