正交增量鞅的平方的分解

The Decomposition of the Square of Martingales with Orthogonal Increments

本文证明,当M为二参数平方可积正交增量鞅时。M^2可分解为鞅和增过程的和,即M^2=A+[M],A为鞅,[M]是M的平方变差。从而解决了Mcrzbach关于M^2的分解问题。应用这个较好的分解我们得到了联系△_JM与△_J[M]的关系式。作为推论,我们简单地证明了Nualart在附加M的连续条件下的分解定理。

In this paper, we prove that if M is a square intcgrablc two-parameter martingale with orthogonal increment, M2 possesses a decompositions by a martingale and increasing process, that is, M2 = A + [M] , here A is a martingale and [M] is the quadratic variation of M. So the problem of the decomposition of E. Merzbach about M2 is solved, with the help of this better decomposition, we prove an equation associated with ΔJM and ΔJ[M]. As a corollary, we prove simply the decomposition theorem under M is continous proved by D. Nualart.