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1、ThispageintentionallyleftblankRANDOMDYNAMICALSYSTEMSThisbookprovidesanexpositionofdiscretetimedynamicprocessesevolv-ingoveraninfinitehorizon.Chapter1reviewssomemathematicalresultsfromthetheoryofdeterministicdynamicalsystems,withparticularempha-sisonapplicatio
2、nstoeconomics.ThetheoryofirreducibleMarkovpro-cesses,especiallyMarkovchains,issurveyedinChapter2.Equilibriumandlong-runstabilityofadynamicalsysteminwhichthelawofmotionissub-jecttorandomperturbationsarethecentralthemeofChapters3–5.Aunifiedaccountofrelativelyre
3、centresults,exploitingsplittingandcontractions,thathavefoundapplicationsinmanycontextsispresentedindetail.Chapter6explainshowarandomdynamicalsystemmayemergefromaclassofdy-namicprogrammingproblems.Withexamplesandexercises,readersareguidedfrombasictheorytothef
4、rontierofappliedmathematicalresearch.RabiBhattacharyaisProfessorofMathematicsattheUniversityofArizona.HehasalsotaughtattheUniversityofCaliforniaatBerkeleyandIndianaUniversity.ProfessorBhattacharyahasheldvisitingresearchprofessorshipsattheUniversityofGoetting
5、en,theUniversityofBielefeld,andtheIndianStatisticalInstitute.HeisarecipientofaGuggenheimFellowshipandanAlexanderVonHumboldtForschungspreis.HeisaFellowoftheInstituteofMathematicalStatisticsandhasservedontheeditorialboardsofanumberofinternationaljournals,inclu
6、dingtheAnnalsofProbability,AnnalsofAp-pliedProbability,JournalofMultivariateAnalysis,EconometricTheory,andStatisticaSinica.Hehasco-authoredNormalApproximationsandAsymp-toticExpansions(withR.RangaRao),StochasticProcesseswithApplica-tions(withE.C.Waymire),andA
7、symptoticStatistics(withM.Denker).MukulMajumdarisH.T.andR.I.WarshowProfessorofEconomicsatCornellUniversity.HehasalsotaughtatStanfordUniversityandtheLondonSchoolofEconomics.ProfessorMajumdarisaFellowoftheEconomet-ricSocietyandhasbeenaGuggenheimFellow,aFordRot
8、atingResearchProfessorattheUniversityofCaliforniaatBerkeley,anErskineFellowattheUniversityofCanterbury,anOskarMorgensternVisitingProfessoratNewYorkUniversity,aLecturerattheCollegedeFrance,andanO
