Chaos decomposition and property of predictable representation (Q1118255)

For the two classes of stochastic processes, namely, martingale difference sequences with constant conditional variances and processes with independent increments, each square-integrable functional of the process has been shown to have chaos decomposition if and only if the process has the property of predictable representation. The definition of chaos is the same as \textit{P. A. Meyer}'s [Eléments de probabilités quantique. Cours Univ. Strasbourg (1984/1985)], that is polynomial functional in discrete parameter case and orthogonal stochastic multiple integral in continuous parameter case. The proofs mainly rely on the necessary and sufficient conditions for the property of predictable representation for these two classes of processes, obtained previously by the authors.