On martingale chaoses. (English) Zbl 1452.60027

Donati-Martin, Catherine (ed.) et al., Séminaire de probabilités XLIX. Cham: Springer. Lect. Notes Math. 2215, 475-494 (2018).
Summary: We extend Wiener’s notion of ‘homogeneous’ chaos expansion of Brownian functionals to functionals of a class of continuous martingales via a notion of iterated stochastic integral for such martingales. We impose a condition of ‘homogeneity’ on the previsible sigma field of such martingales and show that under this condition the notions of purity, chaos representation property and the predictable representation property all coincide.
For the entire collection see [Zbl 1402.60004].


60G44 Martingales with continuous parameter
60H10 Stochastic ordinary differential equations (aspects of stochastic analysis)
60H05 Stochastic integrals
Full Text: DOI


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