1、湖南師范大學(xué)碩士學(xué)位論文擴(kuò)散情形的Feller與強Feller性姓名：李丁申請學(xué)位級別：碩士專業(yè)：概率論與數(shù)理統(tǒng)計指導(dǎo)教師：向開南20090301ABSTRACTFellerpropertyandstrongFelleronearesignificantinthestudyofMarkovprocessesInthispaper，westudythesepropertiesfordiffusionsForthefollowingstoc

2、hasticdifferentialequation(SDE)inR1：dK=盯(K)反比b(Yt)dt，K=z∈R1，ifeitherOkabeShimizuconditionorPerkinsconditionholdsthenanykpointmotion((M(z1)，，K(z七))侖。)(釓m)∈融fortheuniquestrongsolution(K(z))￡≥。totheSDEhasaFellersemigroupon(

3、Co(R七)，I)(seeChapter3)RemovingthedriftterminaboveSDE，weprovethatforany盯∈cb(R1)satisfyingz(a)≠仍and，(盯)=仍，theweaksolutionytotheobtainedSDEisFellerianon(Co(R1)，”II)underamildcondition，butthe互1仃2(z)器diffusionYobtainedbyabsor

4、bingpreviousdiffusionatz(盯)isFellerianon(Co(R1)，”0)withoutadditionalconditions(refertoChapter41Finallythoughthegeneratorofanykpointmotionofstochasticflowswithk≥2isdegeneratedandmaynotbehypoelliptic，itsstrongFellerpropert