随机方程的截断方法综述.pdf

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第３５卷第１期 安　徽　工　程　大　学　学　报 Vol．３５．No．１
２０２０年２月 JournalofAnhuiPolytechnicUniversity Feb．,２０２０
文章编号:１６７２Ｇ２４７７(２０２０)０１Ｇ０００１Ｇ１１
Truncated MethodsforStochasticEquations:
AReview
１, ２
LIU Wei MAO Xuerong
(１．DepartmentofMathematics,ShanghaiNormalUniversity,Shanghai２００２３４,China;
２．DepartmentofMathematicsandStatistics,UniversityofStrathclyde,Glasgow,G１１XH,UK)
Abstract:ThetruncatedEulerＧMaruyama(EM)methodwasoriginallyproposedbyMao(２０１５,J．Comput．
Appl．Math．)．Afterthat,plentyofworksemployedtheideatoconstructnumericalapproximationstodifferＧ
enttypesofstochasticequations．Duetothebloomoftheresearchinthisdirection,wegiveathoroughreview
oftherecentdevelopmentinthispaper,alongwhichwealsopointoutsomepotentialandchallengingresearch．
Keywords:stochasticdifferentequations;superＧlinearcoefficients;truncatedmethods;explicitmethods．
ChineseLibraryClassification:O２１１．６　　　　DocumentIdentification:A
１　Introduction
Inrecentdecades,stochasticdifferentialequations(SDEs)havebeenbroadlyusedtomodeluncerＧ
tainphenomenaindifferentareas,suchasfinance,biology,chemistry,andphysics[１,１２,３４Ｇ３５]．
However,theexplicitclosedformofthetruesolutionisrarelyfound．EvenforlinearSDEs,theirexＧ
plicitexpressionsoftruesolutionsinvolvestochasticintegralsandhencethestatisticalpropertiesofthe
truesolutionsinmostcasescanonlybeseenfromnumericalsimulations．Therefore,numericalmethods
forSDEsbecomeextremelyimportantinapplications．
SincethesolutionstoSDEscanbeunderstoodasstochasticprocesses,theerrorsofnumericalsoluＧ
tionscouldbeinve