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1、LectureNotesinMathematics1499Editors:J.-M.Morel,CachanF.Takens,GroningenB.Teissier,ParisKazuakiTairaBoundaryValueProblemsandMarkovProcessesSecondEdition123KazuakiTairaUniversityofTsukubaInstituteofMathematicsTsukubaIbaraki305-8571Japantaira@math.tsukuba.ac.jpISSN0075-8434e-ISS
2、N1617-9692ISBN978-3-642-01676-9e-ISBN978-3-642-01677-6DOI10.1007/978-3-642-01677-6SpringerDordrechtHeidelbergLondonNewYorkLibraryofCongressControlNumber:2009928104MathematicsSubjectClassification(2000):35J25,47D05,47D07,60J35,35K60cSpringer-VerlagBerlinHeidelberg2009Thisworkis
3、subjecttocopyright.Allrightsarereserved,whetherthewholeorpartofthematerialisconcerned,specificallytherightsoftranslation,reprinting,reuseofillustrations,recitation,broadcasting,reproductiononmicrofilmorinanyotherway,andstorageindatabanks.Duplicationofthispublicationorpartsthereo
4、fispermittedonlyundertheprovisionsoftheGermanCopyrightLawofSeptember9,1965,initscurrentversion,andpermissionforusemustalwaysbeobtainedfromSpringer.ViolationsareliabletoprosecutionundertheGermanCopyrightLaw.Theuseofgeneraldescriptivenames,registerednames,trademarks,etc.inthispu
5、blicationdoesnotimply,evenintheabsenceofaspecificstatement,thatsuchnamesareexemptfromtherelevantprotectivelawsandregulationsandthereforefreeforgeneraluse.Coverdesign:SPiPublisherServicesPrintedonacid-freepaperSpringerispartofSpringerScience+BusinessMedia(www.springer.com)Tothem
6、emoryofProfessorKiyosiItˆo(1915–2008)PrefacetotheSecondEditionThismonographisanexpandedandrevisedversionofasetoflecturenotesforthegraduatecoursesgivenbytheauthorbothatHiroshimaUniversity(1995–1997)andattheUniversityofTsukuba(1998–2000)whichwereaddressedtotheadvancedundergradua
7、tesandbeginning-graduatestudentswithinterestinfunctionalanalysis,partialdifferentialequationsandprobability.Thefirsteditionofthismonograph,whichwasbasedonthelecturenotesgivenattheUniversityofTsukuba(1988–1990),waspublishedin1991.Thiseditionwasfoundusefulbyanumberofpeople,butitwe
8、ntoutofprintafterafewyears.Thissecondeditionhasbeenrevisedtos
