Title

On Martingale Chaoses

Document Type

Book Chapter

Publication Title

Lecture Notes in Mathematics

Abstract

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.

First Page

475

Last Page

494

DOI

10.1007/978-3-319-92420-5_13

Publication Date

1-1-2018

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