Représentation prévisible et changement de temps. (Previsible representation and change of time) (Q1082712)

Let \((M^ i)_{i\geq 0}\) be a sequence of independent local martingales. Suppose that each \(M^ i\) has the property of predictable representation with respect to its natural filtration, that is, each (m,(\({\mathcal F}_ t^{M^ i}))\)-local martingale has the representation \(m=m_ 0+H\cdot M^ i\), where H is a (\({\mathcal F}_ t^{M^ i})\)-predictable process. Suppose that \((A^ i)_{i\geq 1}\) is a sequence of continuous increasing (\({\mathcal F}_ t^{M^ i})\)-adapted processes. The paper gives some sufficient conditions for \(M=M^ 0+\sum_{i\geq 1}M^ i_{A^ i}\) to be a local martingale and for M to have the property of predictable representation with respect to the filtration (\({\mathcal F}_ t^{M^ 0})\vee ({\mathcal F}_ t^{M^ 1_{A^ 1}})\vee ({\mathcal F}_ t^{M^ 2_{A^ 2}})\vee...\).