简介：Inthisnote,wegiveanecessaryandsufficientconditionforviabilitypropertyofdiffusionprocesseswithjumpsonclosedsubmanifoldsofR~m.OurresultisthesystemisviableinaclosedsubmanifoldKiffthecoefficientsaretangenttoKalongKiftheequationisinthesenseofstratonovichintegralandthesolutionjumpsfromKtoK.

简介：<正>Thisnoteisdevotedtothestudyofthestochasticcomparabilityofjumpprocesses.Onthebasisof[2]and[3],itisprovedthattwojumpprocessesarestochasticallycomparableifandonlyiftheirq-pairsarecomparable.Meanwhile,theresultconcerningtheuniquenessgivenin[6]isalsoimprovedupon.

简介：在这篇文章，作者在无限的尺寸在随机的方程的一个班的法律证明唯一，然后，我们使用它建立不变的措施的存在和唯一概括了随机的部分微分方程由L使不安吗？？

简介：AclassofhybridjumpdiffusionsmodulatedbyaMarkovchainisconsideredinthiswork.Themotivationstemsfrominsuranceriskmodels,andemergingapplicationsinproductionplanningandwirelesscommunications.Themodelsarehybridinthattheyinvolvebothcontinuousdynamicsanddiscreteevents.Undersuitableconditions,asymptoticexpansionsofthetransitiondensitiesfortheunderlyingprocessesaredeveloped,Theformalexpansionsarevalidatedandtheerrorboundsobtained.

简介：Inthisarticle,thejointdistributionsofseveralactuarialdiagnosticswhichareimportanttoinsurers’runningforthejump-diffusionriskprocessareexamined.Theyincludetheruintime,thetimeofthesurplusprocessleavingzeroultimately(simply,theultimatelyleaving-time),thesurplusimmediatelypriortoruin,thesupremeprofitsbeforeruin,thesupremeprofitsanddeficituntilitleaveszeroultimatelyandsoon.TheexplicitexpressionsfortheirdistributionsareobtainedmainlybythevariouspropertiesofL′evyprocess,suchasthehomogeneousstrongMarkovpropertyandthespatialhomogeneitypropertyetc,moveover,themanypropertiesforBrownianmotion.

简介：TherepresentationofadditivefunctionalsandlocaltimesforjumpMarkovprocessesareobtained.Theresultsofuniformlyfunctionalmoderatedeviationandtheirapplicationstobirth-deathprocessesarealsopresented.

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简介：Inthispaper,aclassofnewimmersedinterfacefiniteelementmethods(IIFEM)isdevelopedtosolveelasticityinterfaceproblemswithhomogeneousandnon-homogeneousjumpconditionsintwodimensions.Simplenon-body-fittedmeshesareused.Forhomogeneousjumpconditions,bothnon-conformingandconformingbasisfunctionsareconstructedinsuchawaythattheysatisfythenaturaljumpconditions.Fornon-homogeneousjumpconditions,apairoffunctionsthatsatisfythesamenon-homogeneousjumpconditionsareconstructedusingalevel-setrepresentationoftheinterface.Withsuchapairoffunctions,thediscontinuitiesacrosstheinterfaceinthesolutionandfluxareremoved;andanequivalentelasticityinterfaceproblemwithhomogeneousjumpconditionsisformulated.Numericalexamplesarepresentedtodemonstratethatsuchmethodshavesecondorderconvergence.