Timeline for Stochastic integrals as honest martingales -- comparison criterion
Current License: CC BY-SA 3.0
12 events
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| S Nov 5, 2015 at 16:35 | history | suggested | Stéphane Benoist | CC BY-SA 3.0 |
math was not being displayed properly
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| Nov 5, 2015 at 16:23 | review | Suggested edits | |||
| S Nov 5, 2015 at 16:35 | |||||
| Sep 9, 2011 at 23:04 | comment | added | George Lowther | @The Bridge: One response to my statement is to request an example of a martingale whose maximum over a finite time interval is not integrable. Without such an example, my statement and answer to the question is moot. Actually, coming up with an example is easier said than done and I'm not going to do it in a comment, so I'll leave you to think about that... | |
| Sep 5, 2011 at 14:51 | comment | added | The Bridge | @ George : I think I got it now, thank's for your time. | |
| Sep 5, 2011 at 13:59 | comment | added | George Lowther | @The Bridge: yes, "proper" (or honest) martingales are simply martingales, just emphasising the fact that you don't mean local martingales in general. So I don't think you are missing anything there. But, the property that the maximum of rho is integrable is strictly stronger than the martingale property on it's own. | |
| Sep 5, 2011 at 13:44 | comment | added | The Bridge | @George : Ok, though I thought that by Hypothesis the process $\rho$ was a martingale and not only a local martingale. Am I missing something about the definition of honest or proper martingales ? I thought they were only martingales and that the vocable "proper" or "honest" had no real mathematical meaning. | |
| Sep 5, 2011 at 12:42 | comment | added | George Lowther | @The Bridge: No typo. I did mean rho. In fact, the statement about rho implies the same statement about p, by the argument further down in my answer. | |
| Sep 5, 2011 at 11:36 | comment | added | The Bridge | @ George : Is there a type in your first sentence ? You meant $p$ not $\rho$ right ? PS :I will erase this comment as soon as you corrected your post or (more probably) me. | |
| Sep 5, 2011 at 9:44 | comment | added | Grzenio | Very interesting, thanks for a complete answer. I did learn quite a lot about stochastic calculus today! I asked another question with some more specific choice for $a_t$. | |
| Sep 5, 2011 at 9:30 | history | edited | George Lowther | CC BY-SA 3.0 |
Fix html
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| Sep 5, 2011 at 9:26 | vote | accept | Grzenio | ||
| Sep 4, 2011 at 22:18 | history | answered | George Lowther | CC BY-SA 3.0 |