Chaotic expansion of powers and martingale representation (v1.5)
This paper extends a recent martingale representation result of [N-S] for a Levy process to filtrations generated by a rather large class of semimartingales. As in [N-S], we assume the underlying processes have moments of all orders, but here we allow angle brackets to be stochastic. Following their approach, including a chaotic expansion, and incorporating an idea of strong orthogonalization from [D], we show that the stable subspace generated by Teugels martingales is dense in the space of square-integrable martingales, yielding the representation. While discontinuities are of primary interest here, the special case of a (possibly infinite-dimensional) Brownian filtration is an easy consequence.
|Date of creation:||15 Jul 2005|
|Note:||Type of Document - pdf; pages: 22. Martingale representation results for filtration generated by a large class of processes, including Levy processes. (Minor improvements to version 1.4)|
|Contact details of provider:|| Web page: http://econwpa.repec.org|
When requesting a correction, please mention this item's handle: RePEc:wpa:wuwpge:0507009. See general information about how to correct material in RePEc.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (EconWPA)
If references are entirely missing, you can add them using this form.