Introduction.to.Stochastic.Processes.with.R

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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 u
INTRODUCTION TO STOCHASTIC PROCESSES WITH R INTRODUCTION TO STOCHASTIC PROCESSES WITH R ROBERT P DOBROW WILEY Copyright o 2016 by John Wiley Sons, Inc. All rights reserved Published by John Wiley Sons, Inc, Hoboken, New Jersey Published simultaneously in Canada No part of this publication may be reproduced, stored in a retrieval system, or transmitted in any form or by any means, electronic, mechanical, photocopying, recording, scanning, or otherwise, except as permitted under Section 107 or 108 of the 1976 United States Copyright Act, without either the prior written permission of the Publisher, or authorization through payment of the appropriate per-copy fee to the Copyright Clearance Center, Inc, 222 Rosewood Drive, Danvers, MA,(978)750-8400, fax 978)750-4470,oronthewebatwww.copyright.comRequeststothePublisherforpermissionshould be addressed to the Permissions Department, John Wiley sons, Inc, lll River Street, Hoboken, NJ 07030,(201)748-6011,fax(201)748-6008,oronlineathttp://www.wiley.com/go/permissions Limit of liability/ Disclaimer of warranty While the publisher and author have used their best efforts in preparing this book, they make no representations or warranties with respect to the accuracy or completeness of the contents of this book and specifically disclaim any implied warranties of merchantability or fitness for a particular purpose. No warranty may be created or extended by sales representatives or written sales materials. The advice and strategies contained herein may not be suitable for your situation. You should consult with a professional where appropriate. Neither the publisher nor author shall be liable for any loss of profit or any other commercial damages, including but not limited to special, incidental, consequential, or other damages For general information on our other products and services or for technical support, please contact our Customer Care Department within the United States at(800)762-2974, outside the United States at (317)572-3993 or fax(317)572-4002 Wiley also publishes its books in a variety of electronic formats. Some content that appears in print may not be available in electronic formats. For more information about Wiley products, visit our web site at www.wiley.com Library of Congress Cataloging-in-Publication Data: Dobrow. Robert p. author Introduction to stochastic processes with r/ Robert P. Dobrow pages cm Includes bibliographical references and index ISBN978-1-118-74065-1( cloth) 1. Stochastic processes. 2. R( Computer program language)I. Title QC20.7.S8D632016 5192′302855133-dc23 2015032706 Set in 10/12pt, Times-Roman by SPi Global, Chennai, India Printed in the united states of america 10987654321 12016 To my family CONTENTS Preface Acknowledgments List of Symbols and Notation about the companion Website 1 Introduction and review 1.1 Deterministic and stochastic models. 1 1. 2 What is a Stochastic Process? 6 1. 3 Monte Carlo Simulation. 9 1.4 Conditional Probability, 10 1. 5 Conditional Expectation, 18 Exercises. 34 2 Markov Chains: First Steps 40 2.1 Introduction. 40 2.2 Markov Chain Cornucopia, 42 2.3 Basic Computations, 52 2. 4 Long-Term behavior-the Numerical evidence, 59 2.5 Simulation. 65 2.6 Mathematical Induction*. 68 Exercises. 70 CONTENTS 3 Markov Chains for the long term 76 3.1 Limiting Distrib 76 3.2 Stationary Distribution, 80 3.3 Can you find the way to state a? 94 3.4 Irreducible markov Chains. 103 3.5 Periodicity, 106 3.6 Ergodic Markov Chains, 109 3.7 Time Reversibility, 114 3.8 Absorbing Chains, 119 9 Regeneration and the strong markov property 133 3.10 Proofs of limit Theorems*, 135 Exercises. 144 4 Branching processes 158 4.1 Introduction. 158 4.2 Mean Generation Size. 160 4.3 Probability Generating Functions, 164 4.4 Extinction is Forever. 168 Exercises. 175 5 Markov Chain Monte Carlo 181 5.1 Introduction. 181 5.2 Metropolis-Hastings Algorithm, 187 5.3 Gibbs Sampler, 197 5.4 Perfect Sampling*, 20.5 5.5 Rate of Convergence: the Eigenvalue Connection*, 210 5.6 Card Shuffing and Total Variation Distance. 212 Exercises. 219 6 Poisson process 223 6.1 Introduction. 223 6.2 Arrival. Interarrival Times. 227 6.3 Infinitesimal Probabilities. 234 6.4 Thinning, Superposition, 238 6.5 Uniform Distribution. 243 6.6 Spatial Poisson Process, 249 6.7 Nonhomogeneous Poisson Process. 253 6.8 Parting Paradox, 255 Exercises. 258 7 Continuous- Time markov Chains 265 7.1 Introduction. 265 【实例截图】
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