D_∞-APPROXIMATION OF PRODUCT VARIATIONS OF TWO PARAMETER SMOOTH SEMIMARTINGALES  

作　　者：刘继成 

机构地区：[1]DepartmentofMathematics,tIuazhongUniversityofScienceandTechnology,Wuhan430074,China

出　　处：《Acta Mathematica Scientia》2004年第2期235-246,共12页数学物理学报（B辑英文版）

基　　金：Work supported by Project 973

摘　　要：Let X be a two parameter smooth semimartingale and (?) be its process of the product variation. It is proved that (?) can be approximated as D_∞-limit of sums of its discrete product variations as the mesh of division tends to zero. Moreover, this result can be strengthen to yield the quasi sure convergence of sums by estimating the speed of the convergence.Let X be a two parameter smooth semimartingale and (?) be its process of the product variation. It is proved that (?) can be approximated as D_∞-limit of sums of its discrete product variations as the mesh of division tends to zero. Moreover, this result can be strengthen to yield the quasi sure convergence of sums by estimating the speed of the convergence.

关 键 词：Malliavin calculus D_∞-Approximation two parameter smooth semimartingale product variation quasi sure 

分 类 号：O172[理学—数学]