Introduction to stochastic processes with R

505 Pages·2016·10.33 MB·English

by  Robert P. Dobrow

(cid:2)
INTRODUCTION
TO STOCHASTIC
PROCESSES WITH R
(cid:2) (cid:2)
(cid:2)
(cid:2)
(cid:2) (cid:2)
(cid:2)
(cid:2)
INTRODUCTION
TO STOCHASTIC
PROCESSES WITH R
ROBERTP.DOBROW
(cid:2) (cid:2)
(cid:2)
(cid:2)
Copyright©2016byJohnWiley&Sons,Inc.Allrightsreserved
PublishedbyJohnWiley&Sons,Inc.,Hoboken,NewJersey
PublishedsimultaneouslyinCanada
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 01923, [phone], fax
[phone], or on the web at www.copyright.com. Requests to the Publisher for permission should
be addressed to the Permissions Department, John Wiley & Sons, Inc., 111 River Street, Hoboken, NJ
07030, [phone], fax [phone], or online at http://www.wiley.com/go/permissions.
LimitofLiability/DisclaimerofWarranty:Whilethepublisherandauthorhaveusedtheirbesteffortsin
preparingthisbook,theymakenorepresentationsorwarrantieswithrespecttotheaccuracyor
completenessofthecontentsofthisbookandspecificallydisclaimanyimpliedwarrantiesof
merchantabilityorfitnessforaparticularpurpose.Nowarrantymaybecreatedorextendedbysales
representativesorwrittensalesmaterials.Theadviceandstrategiescontainedhereinmaynotbesuitable
foryoursituation.Youshouldconsultwithaprofessionalwhereappropriate.Neitherthepublishernor
authorshallbeliableforanylossofprofitoranyothercommercialdamages,includingbutnotlimitedto
special,incidental,consequential,orotherdamages.
(cid:2) (cid:2)
Forgeneralinformationonourotherproductsandservicesorfortechnicalsupport,pleasecontactour
CustomerCareDepartmentwithintheUnitedStatesat(800)762-2974,outsidetheUnitedStatesat
[phone]orfax(317)572-4002.
Wileyalsopublishesitsbooksinavarietyofelectronicformats.Somecontentthatappearsinprintmay
notbeavailableinelectronicformats.FormoreinformationaboutWileyproducts,visitourwebsiteat
www.wiley.com.
LibraryofCongressCataloging-in-PublicationData:
Dobrow,RobertP.,author.
IntroductiontostochasticprocesseswithR/RobertP.Dobrow.
pagescm
Includesbibliographicalreferencesandindex.
ISBN978-1-118-74065-1(cloth)
1. Stochasticprocesses.2. R(Computerprogramlanguage)I.Title.
QC20.7.S8D632016
519.2′302855133–dc23
2015032706
Setin10/12pt,Times-RomanbySPiGlobal,Chennai,India.
PrintedintheUnitedStatesofAmerica
10987654321
1 2016
(cid:2)
(cid:2)
Tomyfamily
(cid:2) (cid:2)
(cid:2)
(cid:2)
(cid:2) (cid:2)
(cid:2)
(cid:2)
CONTENTS
Preface xi
(cid:2) (cid:2)
Acknowledgments xv
ListofSymbolsandNotation xvii
AbouttheCompanionWebsite xxi
1 IntroductionandReview 1
1.1 DeterministicandStochasticModels, 1
1.2 WhatisaStochasticProcess? 6
1.3 MonteCarloSimulation, 9
1.4 ConditionalProbability, 10
1.5 ConditionalExpectation, 18
Exercises, 34
2 MarkovChains:FirstSteps 40
2.1 Introduction, 40
2.2 MarkovChainCornucopia, 42
2.3 BasicComputations, 52
2.4 Long-TermBehavior—theNumericalEvidence, 59
2.5 Simulation, 65
2.6 MathematicalInduction*, 68
Exercises, 70
(cid:2)
(cid:2)
viii CONTENTS
3 MarkovChainsfortheLongTerm 76
3.1 LimitingDistribution, 76
3.2 StationaryDistribution, 80
3.3 CanyouFindtheWaytoStatea? 94
3.4 IrreducibleMarkovChains, 103
3.5 Periodicity, 106
3.6 ErgodicMarkovChains, 109
3.7 TimeReversibility, 114
3.8 AbsorbingChains, 119
3.9 RegenerationandtheStrongMarkovProperty*, 133
3.10 ProofsofLimitTheorems*, 135
Exercises, 144
4 BranchingProcesses 158
4.1 Introduction, 158
4.2 MeanGenerationSize, 160
4.3 ProbabilityGeneratingFunctions, 164
4.4 ExtinctionisForever, 168
Exercises, 175
5 MarkovChainMonteCarlo 181
(cid:2) (cid:2)
5.1 Introduction, 181
5.2 Metropolis–HastingsAlgorithm, 187
5.3 GibbsSampler, 197
5.4 PerfectSampling*, 205
5.5 RateofConvergence:theEigenvalueConnection*, 210
5.6 CardShufflingandTotalVariationDistance*, 212
Exercises, 219
6 PoissonProcess 223
6.1 Introduction, 223
6.2 Arrival,InterarrivalTimes, 227
6.3 InfinitesimalProbabilities, 234
6.4 Thinning,Superposition, 238
6.5 UniformDistribution, 243
6.6 SpatialPoissonProcess, 249
6.7 NonhomogeneousPoissonProcess, 253
6.8 PartingParadox, 255
Exercises, 258
7 Continuous-TimeMarkovChains 265
7.1 Introduction, 265
(cid:2)