离散n指标下鞅分解定理

DECOMPOSITION THEORMS OF SUBMARTINGALES INDEXED BY N^N

本文讨论各种类型 n 维离散指标下鞅表成适当类型的鞅和增过程之和的问题,得到了相应的充分必要条件,并利用这些基本结果构造一个反例,否定了 Merzbach关于平方可积强鞅的平方必可唯一分解成鞅与可料增过程之和的一个两指标情形的定理.

In this paper,we discuss how to represent uarious kinds of submartingales as the sums of(Pre-dictable)increasing processes and cofresponding kinds of martingales.We find out sufficient and neces-sary conditions.We also use them to construct a counter-example to show that the following statement of Merybach needit hold:for ang double-indexed strong martingale M,M^2 Could be uniquely represe nted by the sum of a martingale and predictable increasing process.