Talk:Martingale representation theorem

WikiProject Statistics (Rated Start-class, Low-importance)

This article is within the scope of the WikiProject Statistics, a collaborative effort to improve the coverage of statistics on Wikipedia. If you would like to participate, please visit the project page or join the discussion.

Start  This article has been rated as Start-Class on the quality scale.
Low  This article has been rated as Low-importance on the importance scale.
WikiProject Mathematics (Rated Start-class, Low-importance)
This article is within the scope of WikiProject Mathematics, a collaborative effort to improve the coverage of Mathematics on Wikipedia. If you would like to participate, please visit the project page, where you can join the discussion and see a list of open tasks.
Mathematics rating:
 Start Class
 Low Importance
Field: Probability and statistics

Untitled

I have proposed deletion for this article. The theorem stated in this way is substantially uncorrect. IMHO, it needs a major re-writing. So, before doing the eventual job, we should decide if this theorem should be on wikipedia or not. If yes, I could eventually work it out. gala.martin (what?) 23:31, 29 April 2006 (UTC)

I agree that the statement of the theorem is poor, but it is a start. Why don't we just rewrite it? Perhaps we could restructure it by the following layout?
1. the statement for continuous martingales and give a few references for the proof,
2. the statement for general martingales, and few references for the proof
3. then perhaps some motivation for it along the lines of saying that Brownian motion is the canonical continuous martingale, while compensated compound Poisson processes are the canonical processes for martingales with jumps and that all martingales are just integrals of a Brownian motion plus some sort of compensated compound Poisson process, and lastly
4. some places where the theorem is used such as in finance where it is used to prove the existence of portfolios AJR_1978

Please, note that discussion about deletion is going on this page (as stated in the template). gala.martin (what?) 17:01, 30 April 2006 (UTC)
↑Jump back a section

Alternative version

Some books refer to the MRT as being the "all cts local martingales are integrals of B.m" version, rather than "all square integrable F_T-measurable random variables are integrals of B.m". For example, Oksendal's "Stochastic Differential Equations" takes this approach, as does Shreve's "Stochastic calculus for finance" and Karatzas and Shreve's "Brownian motion and stochastic calculus" (although K&S doesn't explicitly refer to it by name).

↑Jump back a section

Definition required

Can someone provide a definition of the term "previsible"? In appears in a few other articles, seemingly without definition. Melcombe (talk) 15:06, 17 February 2009 (UTC)

↑Jump back a section
Last modified on 25 February 2013, at 23:13