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 ...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.展开更多
基金Supported by the National Natural Science Foundation of China.
文摘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.
