Acta mathematica scientia,Series B

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

 LIU Ji-Cheng   

  • Online:2004-07-20 Published:2004-07-20
  • Supported by:

    Work supported by Project 973.

Abstract:

Let X be a two parameter smooth semimartingale and ˜X be its process of
the product variation. It is proved that ˜X can be approximated as D1−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.

Key words: Malliavin calculus, D1-Approximation, two parameter smooth semimartin-gale, product variation, quasi sure

CLC Number: 

  • 60H07
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