拟对称马尔可夫过程穿越次数估计.pdfVIP

Vo1．29(2009) 数 学 杂 志 No．2 J．ofMath．(PRC) CRoSS—ESTIM ATE FoR QUASI—SYMMETRICMARKOVPROCESSES HUANG Jin—uring ，JING Yi—wen (1．Dept．ofMath．，2．Dept．o．厂D riceEconomy，MilitaryEconomics Academy．Wuhan 430035，China) Abstract：Theeross—estimateofMarkovprocessesisstudied．Usingtheforward—backward martingaledecomposition．thecross—estimateofquasi—symmetricMarkovprocessesisobtained· and the cross—estimateofLyons—Zheng is extended from the symmetric case to the quasi— symmetriccase． Keywords：forward—backwardmartingaledecomposition；cross—estimate；quasi—symmetric 2000MRSubjcetClassification：60F05；60H10；60J45 Documentcode：A ArticleID ：0255-7797(2009)02—0125—08 1 IntrOducti0n T．J．LyonsandW．A．Zheng[1] used the forward—backward martingale decomposition to prove a cross—estimate for Diriehlet functions along the pathsofa stationarysymmetricdiffusiononR overthetimeinterval[o，1]．Recently，A．Ancona， R．LyonsandY．Peres[2]establishedacrossingestimateforDirichletfunctionsalongthe pathsofa transientsymmetric discrete—time M arkov chain or a transientsymmetric diffusiononaRiemannianmanifold，overthetimeinterval[O，∞]，allowinganarbitrary startingpointfortheprocess．Z．Q．Chen，P．J．FitzsimmonsandR．Song-[3]showedthat across——estimatecanbeestablishedforgeneralsymmetricrightMarkovprocessest‘‘ransient orrecurrent。overafiniteorinfinitetimeinterval，forquasi—everystartingpoint． LetD[O，1]bethespaceofallefidlfigfunctionsdefinedon[O，1]takingvaluesinE． Inthesymmetriccase，P．A．MeyerandW．A．Zheng[4]introducedatightnesscriterion forprobabilitymeasuresonDEO，1]inatopologywhichisweakerthanSkorohod’Sone． T．J．LyonsandW．A．Zheng[1]obtainedundergeneralconditionatightnesscriteriafor measuresonpathspaceassociatedw