Talk:Optional stopping theorem

Undefined symbol: $\land$

What does the symbol $\land$ mean in the condition (c)?

This is the meet. I added a brief description to the text. Zfeinst (talk) 21:05, 11 October 2015 (UTC)

Previous talk

One should add to the proof why E[X₁]=E[X_t^tau], which is the only non-trivial thing in the proof in my opinion. Szepi (talk) 21:59, 24 October 2009 (UTC)

Reference to example section is problematic (as there is not example section). 83.248.213.36 (talk)

The theorem also applies to right-continuous martingales, not just martingales in discrete time.

Of course the proof is somewhat harder but it should at least be mentioned in the article. 77.1.167.9 (talk) 20:28, 17 November 2010 (UTC)

I could be missing something, but it seems like the proof given here is not really correct. In particular, we do not have

$\mathbb {E} \left(\sum _{i=1}^{\tau \land t-1}|X_{i+1}-X_{i}|\right)=\sum _{i=1}^{\tau \land t-1}\mathbb {E} |X_{i+1}-X_{i}|$.

Also, the use of the dominated convergence theorem is a little confusing--it is not relevant that $\mathbb {E} |X_{t}^{\tau }|$ is finite, but rather that $\mathbb {E} \left(|X_{1}|+\sum _{i=1}^{\tau \land t-1}|X_{i+1}-X_{i}|\right)$ is. The hypothesis $\mathbb {E} (|X_{i+1}-X_{i}|)\leq c$ may need to be replaced by $\mathbb {E} (|X_{i+1}-X_{i}|\mid X_{i})\leq c$. (Arghbleargh (talk) 06:44, 18 November 2011 (UTC))

reference section

The link reference given is not accessible (access forbidden). A new source for the facts of the article is needed. Any text book providing an introduction to martingales should do. — Preceding unsigned comment added by Quarague (talk • contribs) 10:45, 2 August 2016 (UTC)

Condition (a) not stated properly

Condition (a) as it is now, is wrong. It should read: The stopping time τ is almost surely bounded, i.e., $\mathbb {P} [\tau <\infty ]=1$.

Otherwise the stopping times defined in the Applications section do not fulfill the requirements.