CHAOS DECOMPOSITION AND PROPERTY OF PREDICTABLE REPRESENTATION
CHAOS DECOMPOSITION AND PROPERTY OF PREDICTABLE REPRESENTATION
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混沌分解和可预测表示的性质
DOI：
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发表时间：
1989
期刊：
影响因子：
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通讯作者：
S. He
中科院分区：
文献类型：
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作者：
S. He
对于两类随机过程，即条件方差为常数的鞅差序列和增量独立的随机过程，证明了该过程的每个平方可积泛函具有混沌分解的充要条件是该过程具有可预测表示性质。混沌的定义与P.A.Meyer的定义相同，即在离散参数情况下是多项式泛函，在连续参数情况下是正交型随机重积分。证明主要依赖于作者以前得到的这两类过程的可预测表示性质的充要条件。
For the two classes of stochastic processes, namely, martingale difference sequences withconstant conditional variances and processes with independent increments, each square-inte-grable functional of the process has been shown to have chaos decomposition if and only ifthe process has the property of predictable representation. The definition of chaos is thesame as P. A. Meyer's, that is polynomial functional in discrete parameter case and ortho-gonal stochastic multiple integral in continuous parameter case. The proofs mainly rely onthe necessary and sufficient conditions for the property of predictable representation forthese two classes of processes, obtained previously by the authors.