简介:在这篇论文,我们考虑Markov进程(X~∈(t),Z~∈(t))相应于有小参数∈的一个微弱地联合的椭圆形的PDE系统>0。我们首先证明那(X~∈(t),Z~∈(t))由联合方法有Feller连续性,然后证明那(X~∈(t),Z~∈t))由收养的Lyapunov不平等有不变的措施μ~∈(·)。最后,当小参数∈趋于到零,我们为μ~∈(·)建立一个大偏差原则。
简介:InthispaperweprovideaprobabilisticapproachtothefollowingDirichletProblem{(∑x4(αijxj)+∑bixi+ξ)u=0,iDu=g,onD,withoutassumingthattheeigenvaluesoftheoperator∑xi(αijxj)+∑bixi+ξwithDirichletboundaryconditionsareallstrictlynegative.TheresultsofthispapergeneralizedthoseofMa.
简介:Inthispaper,wederivetwogeneralparameterizedboundariesoffinitedifferenceschemeforVee’sPDEwhichisusedtopricebothfixedandfloatingstrikeAsianoptions.Usingthesetwoboundaries,wecandealwithallkindsofsituations,especially,someextremecases,likeoverhighvolatility,verysmallvolatility,etc,underwhichtheAsianoptionisusuallymispricedinmanyexistingnumericalmethods.Numericalresultsshowthatourboundariesareprettyefficient.
简介:Inthisworkweconsidertheproblemofshapereconstructionfromanunorganizeddatasetwhichhasmanyimportantapplicationsinmedicalimaging,scientificcomputing,reverseengineeringandgeometricmodelling.ThereconstructedsurfaceisobtainedbycontinuouslydeforminganinitialsurfacefollowingthePartialDifferentialEquation(PDE)-baseddiffusionmodelderivedbyaminimalvolume-likevariationalformulation.Theevolutionisdrivenbothbythedistancefromthedatasetandbythecurvatureanalyticallycomputedbyit.Thedistancefunctioniscomputedbyimplicitlocalinterpolantsdefinedintermsofradialbasisfunctions.SpacediscretizationofthePDEmodelisobtainedbyfiniteco-volumeschemesandsemi-implicitapproachisusedintime/scale.Theuseofalevelsetmethodforthenumericalcomputationofthesurfacereconstructionallowsustohandlecomplexgeometryandevenchangingtopology,withouttheneedofuser-interaction.Numericalexamplesdemonstratetheabilityoftheproposedmethodtoproducehighqualityreconstructions.Moreover,weshowtheeffectivenessofthenewapproachtosolveholefillingproblemsandBooleanoperationsbetweendifferentdatasets.
简介:从量化的角度,引入了风险和违约等信用概念的数学描述。应用概率论、随机过程和微分方程的数学工具,讨论了金融和信用风险的数学模型以及应用。
简介:本文在空间X_K~(r,q)中研究三维带有科氏力的不可压缩流体Navier-Stokes方程(αu)/(αt)-Δu+ωe_3×u+(u·▽)u+▽q=f(x,t)∈R~3×Rdivu=0(x,t)∈R~3×R证明对于小的殆周期外力f∈BUC(R;B_(p,2)~(-s)(R~3))∩BUC(R;L~l(R~3)),该系统存在唯一的殆周期mild解.