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简介：<正>SupposeXisasuperdiffusioninRdwithgeneralbranchingmechanism￠.andYDdenotesthetotalweightedoccupationtimeofXinaboundedsmoothdomainD.WediscusstheconditionsonψtoguaranteethatYDhasabsoluteycontinuousstates.Andforparticularψ（z）=z(l+,0DisabsolutelycontinuouswithrespecttotheLebesguemeasureinD.whereasinthecased>2+2/B.itissingular.AsweknowtheabsolutecontinuityandsingularityofY(Dhavenotbeendiscussedbefore.

简介：SupposethatXtistheFleming-ViotprocessassociatedwithflactionalpowerLaplacianoperator-(-△)^α/20<α<2andYt=∫^t0Xsdsistheso-calledoccupationtimeprocess.Inthispaper,theasymptoticbehavioratalargetimeantitheabsolutecontinuityofYiareinvestigated.

简介：<正>ThispaperdevelopsasymptoticpropertiesofsingularlyperturbedMarkovchainswithinclusionofabsorbingstates.Itfocusesonbothunscaledandscaledoccupationmeasures.Undermildconditions,amean-squareestimateisobtained.Byaveragingthefastcomponents,weobtainanaggregatedprocess.Althoughtheaggregatedprocessitselfmaybenon-Markovian,itsweaklimitisaMarkovchainwithmuchsmallerstatespace.Moreover,asuitablyscaledsequenceconsistingofacomponentofscaledoccupationmeasuresandacomponentoftheaggregatedprocessisshowntoconvergetoapairofprocesseswithaswitchingdiffusioncomponent.

简介：1.IntroductionMotiffedbysomelargedeviationresultsforbranchingparticlesystem,thelargedeviationresultsforsuperprocesseshavebeeninvestigatedrecently.CoxandGffeathll]startedtheinvestigationofthelargedevistionforcriticalbranchingBrochanmotion.IscoeIZIcarr...

简介：Fora〈r〈b,theapproachofLiandZhou（2014）isadoptedtofindjointLaplacetransformsofoccupationtimesoverintervals（a,r）and（r,b）foratimehomogeneousdiffusionprocessbeforeitfirstexitsfromeitheraorb.Theresultsareexpressedintermsofsolutionstothedifferentialequationsassociatedwiththediffusionsgenerator.Applyingtheseresults,weobtainmoreexplicitex-pressionsonthejointLaplacetransformsofoccupationtimesforBrownianmotionwithdrift,BrownianmotionwithalternatingdriftandskewBrownianmotion,respectively.

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