资源描述：
《large deviations for perturbed reflected diffusion processes》由会员上传分享，免费在线阅读，更多相关内容在工程资料-天天文库。
1、Stochastics:AnInternationalJournalofProbabilityandStochasticsProcessesVol.81,No.6,December2009,531–543LargedeviationsforperturbedreflecteddiffusionprocessesabLijunBoandTushengZhang*abDepartmentofMathematics,XidianUniversity,Xian710071,P.R.China;DepartmentofMathematics,Universi
2、tyofManchester,OxfordRoad,ManchesterM139PL,UK(Received12December2006;finalversionreceived3February2008)Inthisarticle,weestablishalargedeviationprincipleforthesolutionsofperturbedreflecteddiffusionprocesses.ThekeyistoproveauniformFreidlin–Ventzellestimateofperturbeddiffusionproce
3、sses.Keywords:largedeviations;perturbeddiffusionprocesses;uniformFreidlin–VentzellestimatesAMSSubjectClassification:60F10;60J271.IntroductionDoneyandZhang[5],obtainedtheexistenceanduniquenessofthesolutionsforthefollowingperturbeddiffusionandperturbedreflecteddiffusionequations:ð
4、tðtXt¼xþsðXsÞdBsþbðXsÞdsþasupXs;t[½0;1ð1:1Þ000#s#tandðtYt¼yþaðYsÞdBsþasupYsþLt;t[½0;1;ð1:2Þ00#s#twherea[ð0;1Þ,x[R;y[Rþaredeterministic,b;s:R!Randa:Rþ!RareboundedLipschitzcontinuousfunction,{Lt;t[½0;1}isnon-decreasingwithL0¼0andðtx{Ys¼0}dLs¼Lt;t[½0;1:0Wemaythinkof{Lt;t[½0;1}the
5、localtimeofthesemimartingale{Yt;t[½0;1}atpointzero.{Bt;t[½0;1}isa1DstandardBrownianmotiononacompletedprobabilityspaceðV;F;ðFtÞt$0;PÞ.TheperturbedreflectedBrownianmotionwasfirstintroducedbyLeGallandYor[7,8],andsubsequentlystudiedbyCarmonaetal.[2,3],PermanandWerner[11]andChaumonta
6、ndDoney[4].Considerthesmallnoiseperturbationsof(1.1)and(1.2):ðtðtpffiffiffiX1¼xþ1sðX1ÞdBþbðX1ÞdsþasupX1;t[½0;1;ð1:3Þtssss000#s#t*Correspondingauthor.Email:tzhang@maths.man.ac.ukISSN1744-2508print/ISSN1744-2516onlineq2009Taylor&FrancisDOI:10.1080/17442500801981084http://www.informawo
7、rld.com532L.BoandT.ZhangandðtpffiffiffiY1¼yþ1aðY1ÞdBþasupY1þL1;t[½0;1:ð1:4Þtssst00#s#tTheaimofthispaperistoestablishalargedeviationprinciple(LDP)forthelawsofX1andY1onthespaceofcontinuousfunctionsequippedwithuniformtopology,respectively.OurapproachwillbebasedonaclassicalresultofAze
8、ncott[1],whichcanbestatedasfollows:1Proposition1.1.LetðEi;diÞ
