The chaotic representation property of compensated-covariation stable families of martingales
The chaotic representation property relates square integrable functionals of some random measure to iterated or multiple integrals. This paper studies a family \(\mathscr X\) of square integrable martingales which is compensated-covariation stable, i.e., such that for any two elements of \(\mathscr X\) the covariation has deterministic compensator and the compensated martingale so obtained is again a member of \(\mathscr X\). The main result of the paper shows that if the set of monomials generated by the given family is total in \(L^2\), then \(\mathscr X\) possesses the chaotic representation property.
scientific article; zbMATH DE number 6674843