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

摘要/Abstract

摘要：

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.

Abstract:

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

中图分类号:

60H07

刘继成. D∞-APPROXIMATION OF PRODUCT VARIATIONS OF TWO PARAMETER SMOOTH SEMIMARTINGALES[J]. 数学物理学报(英文版), 2004, 24(2): 235-246.

LIU Ji-Cheng. D∞-APPROXIMATION OF PRODUCT VARIATIONS OF TWO PARAMETER SMOOTH SEMIMARTINGALES[J]. Acta mathematica scientia,Series B, 2004, 24(2): 235-246.

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