iEssentialsofStochasticProcessesRickDurrett304050607010‐Sep10‐Jun10‐Mayatexpiry01020500520540560580600620640660680700AlmostFinalVersionofthe2ndEdition,December,2011Copyright2011,Allrightsreserved.iiPrefaceBetweenthefirstundergraduatecourseinprobabilityandthefirstgraduatecoursethatusesmeasuretheory,thereareanumberofcoursesthatteachStochasticProcessestostudentswithmanydifferentinterestsandwithvaryingdegreesofmathematicalsophistication.Toallowreaders(andinstructors)tochoosetheirownlevelofdetail,manyoftheproofsbeginwithanonrigorousanswertothequestion“Whyisthistrue?”followedbyaProofthatfillsinthemissingdetails.Asitispossibletodriveacarwithoutknowingabouttheworkingoftheinternalcombustionengine,itisalsopossibletoapplythetheoryofMarkovchainswithoutknowingthedetailsoftheproofs.Itismypersonalphilosophythatprobabilitytheorywasdevelopedtosolveproblems,somostofoureffortwillbespentonanalyzingexamples.Readerswhowanttomasterthesubjectwillhavetodomorethanafewofthetwentydozencarefullychosenexercises.ThisbookbeganasnotesItypedinthespringof1997asIwasteachingORIE361atCornellforthesecondtime.InSpring2009,themathematicsdepartmentthereintroduceditsownversionofthiscourse,MATH474.Thisstartedmeonthetaskofpreparingthesecondedition.TheplanwastohavethisfinishedinSpring2010afterthesecondtimeItaughtthecourse,butwhenMayrolledaroundcompletingthebooklostouttogettingreadytomovetoDurhamafter25yearsinIthaca.IntheFallof2011,ItaughtDuke’sversionofthecourse,Math216,to20undergradsand12graduatestudentsandovertheChristmasbreakthesecondeditionwascompleted.Thesecondeditiondifferssubstantiallyfromthefirst,thoughcuriouslythelengthandthenumberofproblemshasremainedroughlyconstant.Throughoutthebooktherearemanynewexamplesandproblems,withsolutionsthatusetheTI-83toeliminatethetediousdetailsofsolvinglinearequationsbyhand.MystudentstellmeIshouldjustuseMATLABandmaybeIwillforthenextedition.TheMarkovchainschapterhasbeenreorganized.ThechapteronPoissonprocesseshasmovedupfromthirdtosecond,andisnowfollowedbyatreatmento...
