Chaotic expansion of powers and martingale representation (v1.5)
AbstractThis 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.
Download InfoIf you experience problems downloading a file, check if you have the proper application to view it first. In case of further problems read the IDEAS help page. Note that these files are not on the IDEAS site. Please be patient as the files may be large.
Bibliographic InfoPaper provided by EconWPA in its series GE, Growth, Math methods with number 0507009.
Length: 22 pages
Date of creation: 15 Jul 2005
Date of revision:
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://126.96.36.199
Martingale representation; stochastic integration; stable subspaces; power brackets; Teugels martingales; polynomial; chaos; Hilbert space direct sum decomposition; Levy processes; finite moements semimartingales; dense.;
Find related papers by JEL classification:
This paper has been announced in the following NEP Reports:
You can help add them by filling out this form.
reading list or among the top items on IDEAS.Access and download statisticsgeneral 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.